Ban evasion so you can continue your triad against another user for their completely innocuous post definitely justifies a permanent ban from that single community.
I agree with that other user, go touch grass. You can use that time to do a lot more for animal rights than arguing with random Lemmy users ever will.
I believe you've misunderstood the exchange, which is understandable as it's not that clear. Op clarified in another comment that they were informing the mod that another user was ban evading.