You aren't part owner, you are a tenant. You pay rent because the place you rent needed a significant investment to to get put in place, and the value of rent is a percentage above the base monthly overhead for the unit because of taxes, maintenance and any utility that is handled by the landlord in general.

If you want to own, go get your own mortgage. Fun fact, any place that's around $100 K or so will have a lower mortgage for it's size than what you'd rent for equivalent.