This is just semantics. Companies are often called services because they operate and maintain the network of service to your house, whether it's electric fields moving around, gas particles, laundry pick up and delivery, trash and recycling, milk, newspaper delivery, Internet service, cable subscription, whatever else. Perfectly reasonable to call home electricity a service operated by your utility.
No argument there. If you're off the grid you're not getting electricity service to your house by a utility. Same if you buy your own milk at the store.
You can still be on the grid and produce your own electricity. The electric company will even buy extra electricity from the consumer.
Electricity or milk is a good. Milk delivery or electricity delivery is a service that delivers a good.
No way you'd say "Milk" was a service, just like you shouldn't say "Electricity" is a service. If you give more detail that makes it a service, then it would be a service.
It was a bullshit question and the teacher didn't want to admit that.
Definitely a bullshit question. Yes, "Electricity" is not a service without context like you said. But if I said what services does your house have? You could say "electricity" if you're connected to an electricity service