Don't parents usually want their child to move out when they get old?

Not particularly, I eloped and left my parents but they are glad for my older brother (24) to live with them as long as he wants to. Also, my brother in law who is 23 and has two kids still lives with his parents. If you want to live with your parents and they are good with it, then go for it. 

maybe your parents will miss you if you move out

Every family is different. If parents and adult children all think it's a good idea to share a home, I don't see where it's anybody else's business -- no matter what the ages are. Ditto for sharing a home with grandparents, siblings, and so on. Who better than family?

Nope, we want our kids and families to stay with us forever, but we know that is nt what is best for them. They need to get out on their own so they can actuly grow into their best selves. 

Some kids we want out, they are a pain in the ***, but we worry when they are gone.

Kids stay at home in different cultures for much different time periods. To each thier own.

Yes, most parents want their children to be independent adults. 

Its different for everyone. In some cultures, you don't move out until marriage, or getting a successful career. And some parents have a tough time dealing with their kids leaving because they're so used to having them there, I knew this guy Spencer who moved out at 25 and his parents immediately divorced and his dad moved to Brazil. Also some moms especially have a lot of trouble even thinking about the idea that they won't have someone to take care of and will always try to get their kids to stay longer. Anyway you ultimately should do whats best for you, and if you're sensing it's time to move on and get your own place you probably should.