> Yes that's what vegetarian means, 99% of the time.

What’s your source for that claim? I know plenty of vegetarians and there’s not a single one where I could assume they eat both dairy and eggs. I don’t think any of them drink milk (oat drinks and the like are common), only some eat cheese, in very varying quantities (from regularly to almost never), same with eggs.

You are assuming what your parent commenter does.

> animals who are farms for milk and eggs are treated just as badly

Again, you have no idea what your parent commenter does. With eggs in particular, there are different tiers related to the animals’ conditions. It is possible to make more ethical choices.