What does China achieve from invading Taiwan?

One, it completes one of their long standing policy of "one China". They still view Taiwan as a rogue rebellion state to bring back into the fold, not an independent country to conquer.

Two, it would cripple a lot of the west's high end silicon industry. TSMC is the only one that can make the worlds most advanced nodes, as well as Taiwan holds chip packaging infrastructure that any other nodes require on to be useful.

To that end it is a geopolitical chip that China can use to pressure the west, but likely will never act upon until a real hot war breaks out.

The premise of your question is all wrong. It centers western control of Taiwan as a natural status quo, and so paints every challenge of that control as a provocation or threat.

Advocating for Taiwan’s sovereignty is not the same as advocating for Taiwan’s continued fealty to the west.

You are approaching this from the perspective of a rational peaceful person from the west, where usually the economy is number one in everything.

Xi has achieved unrivaled rule over the party. He has successfully established a police state that ensures that any domestic dissent is immediately crushed with brutal efficiency. He has subjugated the provinces that dared to think about self rule and cultural differences, and is in the process of ethnic cleansing without any significant opposition or consequences. He has gained colonial influence all over Africa through economic means. He has taken over Hong Kong. He has significantly modernized and expanded the military, including nuclear weapons. He had made China into a global economic superpower, which other countries, including rivals, depend on for a significant amount of manufactured goods and resources.

So what is left for him? Surely he is not a man who can be content with what he has.

The obvious next step is to make China into a military superpower. For that you need to exert power abroad. What better place to begin with than that small island just off your coast that has been a challenge to Chinese supremacy for decades?

Of course, Taiwan is kind of protected by the US, the dominant superpower of the time. But they are struggling, looking weak. If China manages to take Taiwan, they will not only have removed that thorn in their side, they will also have punched the biggest, meanest kid on the block on the nose and gotten away with it.

The giant American military base next to China falls.

Also Taiwan claims to be part of China. And America claims Taiwan is part of China.

From China's geopolitical standpoint:

Taiwan lies between China and the Pacific Ocean.

Taiwan is part of the First Island Chain (which includes Japan, Taiwan, Philippines) — many of these are U.S.-aligned or host U.S. bases.

Control over Taiwan would:

Give China greater military and surveillance reach into the Pacific.

Potentially allow it to break out of U.S.-aligned containment.

Give it more control over critical sea lanes and access to deeper waters (vital for its navy).

In 100 years, long after the United States has broken into Baltic states, there will be a reunification movement and people will ask "why do they want to invade Texas?". There will be politicians who's whole political careers will be built on the promise they can make the United States one country again. Understand this and you will understand China and Taiwan.

Lots of good points, but one aspect that people haven't mentioned yet is that Taiwan is part of the "first island chain"

https://en.wikipedia.org/wiki/Island_chain_strategy

If the PRC conquers Taiwan, then it makes it much harder for the west to blockade the PRC in future conflicts.

Though technically, it is much more important to control the strait of Malacca than Taiwan.

https://en.wikipedia.org/wiki/Malacca_dilemma

Land and the sea surrounding Taiwan, which comes with resource that they can exploit, and controling people that they claim is theirs. It's the same reason why europe sail across the sea to colonize others land, and why US doesn't let Puerto Rico become independent. China never acknowledged that Taiwan is an independent country, they always believe that Taiwan is their territory. It's imperialism.

china is a bit like Yugoslavia before the end: lots of different ethnicities being forced to be together. letting a country made up of Chinese people exist in parallel to china keeps a flame of hope alight for those 51 non-Han Chinese ethnicities that were forced to be part of continental china. and China has struggled immensely with multitudes of local kingdoms and warlords throughout its history so it is afraid as its people are very aware of this past through historical dramas

It's a staging area for the US that's very close to China, so there's that reason strategically. But really, there's not a lot of reason to which is why they haven't done so already. China is, as far as I'm aware, perfectly happy with the traditional US approach towards Taiwan, a policy of "strategic ambiguity" that doesn't officially recognize Taiwan as independent (while informally supporting them) and which has kept the peace for many decades. China does not gain much from provoking a military confrontation with the US, as things stand, China is winning the peace through economic development while the US is going all in on the military. By maintaining the status quo, China can leave the issue open and kick the can down the road, maintaining the possibility that someday in the future they may be in a strong enough position to press the issue.

Even still, China now has its own academia and engineering, and is larger than Taiwan. Hence, even without the corporate espionage mainland China is known for, wouldn’t investing in their burgeoning semiconductor industry make more sense, rather than spending that money on war?

That's exactly what they've been doing. That article mentions that they've actually recruited 3000 engineers from Taiwan's chip industry to help develop their own chips.

Yet while taking Taiwan would mean access to deep-water ports, it’s not as though Taiwan would ever pose a threat to Chinese power projection—their stance is wholly defensive. If China decided to pull an “America” and send a carrier to the Middle East or something, no one would stop them and risk a war.

Taiwan's stance is defensive, but the same isn't necessarily true of the US, which operates in Taiwan. The US has recently started throwing around rhetoric and shifting spending focuses towards treating a hot war with China as a serious possibility, insane as it may be. This is (hopefully) just bluster to justify defense spending, but I'm not at all convinced that if China sent a carrier to the Middle East, the US would not retaliate. If anything, they're looking for a reason.

Even if taiwans technology manufacturing gets destroyed in the invasion, it's still major part of western world's component infrastructure. They can also just rebuild. China gaining control over that or even just denying it to west would make china internationally more powerful no matter how it goes.

Most likely that isnt the only reason they want taiwan, but i dont believe it isnt one of them.

What does China achieve

The typical bully's satisfaction.

Same thing they gained from invading Hong Kong, they think it belongs to them.

Or as one of my old friends told me while playing Final Fantasy 12; the only legitimate reason to wage war against another country - land.

Hong Kong is already part of the Chinese mainland and was already kinda part of China, but Taiwan is a geographically strategic location that puts both Koreas, the Philippines, & Japan in a tougher position. Even without war it would make trade and travel in the Pacific much harder.

Taiwan is a fantastic launching point for an invasion of China and Taiwan has decent relations with the US and other capitalist states who have an interest in opposing China. Yk how people say Israel is an unsinkable aircraft carrier in the middle east? Taiwan could be like that for China if the western powers decided to use it as such. There is already a US military base there. Imagine how the US would react if Cuba had a Chinese military base? This is the main material reason.

Chip manufacturing could also play a role but it is a minor one compared to this.

The gamble just doesn’t really seem worth it.

China is not invading Taiwan. However if it comes to a war with the US, then it really has to take out Taiwan. It is just too close to the mainland, allowing for easy bombing and missile attacks, while als being able to cut off shipping from the mainland. Obviously the US likes that a lot, as it makes war against the US much more costly for China.

At the same time leaders often make horrible decisions. Just look at the US invading Iraq and Afghanistan or Russia invading Ukraine. Clearly not good wars for the countries invading, but they still did it.

Imo I think the biggest thing is it would be completing the revolution in the sense that the KMT fled to Taiwan and is a holdout, that would be a huge win for national pride and legitimacy for the government. The second biggest thing would be nothaving another country with an army so close to them that is "hostile" to their interests. And then after that there would be a lot of other benefits like absorbing their industry, economic zones, military bases, etc. They would much rather have the modern KMT party win an election and vote to become a part of China, than invade, which while very unlikely is not impossible by any means in the span of decades.

Evil, Scary China Refuses To Passively Let Us Encircle It: Notes From The Edge Of The Narrative Matrix – Caitlin Johnstone

That's a pretty good article explaining it. The funny thing is that the US media is always framing China as the aggressor. But one look at that map, like with your real eyes, not the crazy eyes, should show you the US is way out there on someone else's doorstep and who the aggressor is. That's just geography.

Personally I don't think China is going to invade Taiwan unless things escalate further. For example, the Russian perspective on the Ukraine is that the US supported the regime change through the NED, helped far right elements overthrow the democratically elected regime and then supported their stance to ban Russian language, oppress Russian speaking populations in Ukraine and supplied them with massive amounts of arms and intelligence. All of this is true historical fact. And in that situation even the chief of NATO Stoltenberg publicly said that Russia launched a "preemptive war" in response to this quasi-NATO membership right on their doorstep. If the US does the same with Taiwan, China might invade. That particular gabit is rather unlikely to succeed in Taiwan though, and Taiwan is far less dangerous to China than a hostile well supplied Ukraine is to Russia (only like 500 miles from Moskow). The smart play for China if that happens is to play rope-a-dope until the US gets tired. Kinda what Iran is doing about the numerous provocations and acts of war against them.

Stopping american influence

Taiwan is a single point of failure for chip manufacturing in the world I don't think annexation would destroy all the chip fabs I think they would still exist and they would be Chinese

lemmitors: They hate Taiwan for their freedom!

The same Russia gained from invading Ukraine, I guess: securing themselves from future, final NATO aggression by proxy.

China considers taiwan a part of its country. If china is able to capture and integrate taiwan into it then it will show that china has become a superpower. If china can capture taiwan then it will show USA and west that china is not a paper tiger.

it's like Spain wanting Catalonia to be under control. Why would Spain want to lose control of a part of their own country?

Street cred.

Extreme disdain for democracy. Some psychopaths want to bring us back before the age of enlightement, while using enlightement or (especially in case of China) post-enlightement ideas to do so, because we citizens are all like badly behaving 12 year olds, who need 24 hour supervision on every day on the week, every month of the year, or we might "go insane" from doing something a psychopathic madman does not want us.