When you are paying the mortgage, you are actually building equity for yourself. It starts slowly at first, as most of your first mortgage payments go towards interests (especially on 30-year loans) but year after year, your equity portion increases and you are essentially paying yourself for living in your own home.
I recently purchased a half-million dollar home with mostly cash because I had my previous home mostly paid off and so was able to put 75% down on this house. Now some would argue that I could have done just as well if paid a landlord rent for the past 20 years and socked the extra money into a bank each month. But I don't think so. I just would have used most of the extra money to go out to dinner more or get a fancier car. Also, in order to save money by renting, I would have had to settle for a smaller living space and would have had to depend on somebody else to do my repairs and maintenance for me. If I wanted to do any remodeling to make the inside look nicer, I'd have to ask permission of the landlord. But then again, why would I want to remodel my apartment on my own dime when I could get evicted at anytime?
Better to pay yourself and have your own place to fix up and remodel as you like.
With the exception of the high-end rental market, your apartment is likely to have a "slummy" feel to it. Most tenants have a "landlord'll take care of it" attitude and so nothing proactive ever gets done unless the landlord hires a landscaper to cut grass and plant a few flower beds or do some carpeting and painting. But it's all done on the cheap. Not the best quality paint will be used and the carpeting will be plain vanilla.
An interesting experiment was done at my company a while back to prove a point (charging our customers for services instead of giving them away for free). We have regional manager's meetings on a regular basis and at these meetings, each manager is handed a package at hotel check-in that included leather binder for taking notes at the meetings, company logo pens, company T-shirts and other such freebies.
Well when these meetings end, about half the managers leave behind the leather binders and most of the freebies end up in the trash.
This one time, each manager got charged $20 for the package. There was a lot of grumbling and complaining about that. But guess what, not a single leather binder was left behind after the meetings and virtually none of the other trinkets were thrown away. This is because these items now had value to these managers because they had to pay for them.
So it is the same with owning a home instead of just renting an apartment. In your own home, you are going to be careful about putting a hole in the wall to hang a picture (you will actually look to see where the studs are) or replacing a fuse properly instead of just jamming a penny in the slot. If you are going to remodel your kitchen, you are going to spend the extra money and get Jenn-Air appliances instead of whatever Home Depot has on sale that week and you will install quality flooring, cabinets, etc.
This statement is correct, but there's an underlying reason why the monthly cost to purchase and own a home is almost always much higher than the monthly rent on the exact same home. If you buy a home today, you're paying a purchase price based on the real estate market today. If you rent that home, the rent your landlord charges will be based on an amortized purchase price that could date back years -- even decades.
This is because in many ways the real estate market is just as fouled-up as the market for buying new cars. If a home was built 20 years ago and it sold for $X to the original buyer, then is there any reason tied to sound economics why that the second owner would pay 20%, 40% or even more for the home today -- after it has aged and deteriorated for 20 years?
You don't need to build equity in your home to do this. In fact, building equity in your home actually flies in the face of one of the most important principles of finance that has gotten a lot of attention in recent decades (after Harry Markowitz was awarded the Nobel Prize in Economics for his work in this area): diversification.
From a purely financial perspective, a home is one of the least diversified (and most illiquid, I might add) investments you can ever own. More than anything else, it truly is a case of "putting all your eggs in one basket."