My dad wanted me to move out when I was 16 or 17
You should move out of your parent's house when you're financially ready to. Don't rent, buy. Living at home will allow you to buy your first place, instead of renting and paying someone elses mortgage.
If you're still 40 and living at home, that's a concern; you should have to your life in order by then, I would hope.
Time is now
Every cricumstance is different. I was 18.