Renting is always more expensive for the monthly payment and generally overall since you don't ever "get" anything for the rent other than shelter for the term of the lease - no long term tangible asset, just a temporary benefit.
You are paying the LL an amount that covers their note, property taxes, maintenance costs (or that builds a maintenance fund), depreciation, etc. The difference is that you don't have to buy the property or qualify for a loan - it's "easier" to get a yearly lease than it is to get a 10/15/20/30 year mortgage loan, and you don't have to come up with a significant down payment - a deposit is usually less than what you'd need to pay towards an owned property. So, the initial pay out is typically lower, but the ongoing payments are always higher.
On top of that, you don't get any tax benefit from renting, but, in the US, at least, you do get a benefit from owning. You get to take a Federal individual income tax deduction, and usually a deduction against state taxable income in the 41 states that have one, for the property tax and mortgage interest you pay - things changed a little a few years ago with what I think is called the "earned income deduction" but there is still a benefit from it.
As for kids getting kicked out at 18 (not your statement, I know), that isn't the norm by a long shot. Usually kids stay with their parents through college, trade school, or until they have a job that allows them to move out and afford a place of their own or a place to share. Often enough, the kids will get out as soon as they can, either because they feel they need to take responsibility for their own lives, or because they can't stand living with their parent's rules. Some may go military as well. Kids getting "kicked out" are usually the kind of individuals that have decided to rebel and become a problem - stealing from their parents to support a drug habit, or simply just goofing off all the time, thinking it's their right to play video games, not work, and eat the food paid for by their parents. If you're an adult, act like one - not a 18-40 year old toddler.