From my personal experience, I moved out of my parents' house as soon as I was able to (went off to college and when I came home I moved in with my then-boyfriend, now-husband). I could not stand living with my parents and even when I go over there for dinner/laundry for just a few hours, I still get annoyed by them and am glad I moved out when I did. All they do is watch the same TV shows or sports over and over and the BICKERING. Not to mention that they like to think that they're poor and trying to save money on stupid things (my Dad apparently doesn't like to leave the lights on so it's always very dark) yet spend it frivolously on other things (going out to eat ALL THE TIME and not to cheap places).
For some people living with their parents can work out, I guess. I have several friends my age that still live with their parents and never moved out or moved out briefly. There are definitely benefits to it, such as not having to pay rent which is ridiculously high right now. But there are also cons of having much less privacy.
My husband and I have briefly considered moving in with his mom mainly for money/house reasons. The only reason we can't is because his uncle is currently living there and he's annoying and the house would be way too cramped at that point. It would have been beneficial though since we could have used the money we're currently spending on rent to help fix up her house. Well, his mom is kind of annoying too, but not in the same way my parents are.
So, yeah, I'm just rambling about my personal experience, but the point is it works in some situations for some people and doesn't work in other situations.
Also, it is your parents house and you need to respect that. Their house, their rules. And if they want to kick you out, then they have the right to do that, unless if you have a lease signed with them and are paying rent to them. I obviously don't know their reasoning, but I'm sure they'd like more privacy and more of their own space.