Let's say you borrow $5 from a friend until you get paid on Friday. You purchase a happy meal and consume it. Only a retard would say that your friend owns the happy meal until you pay him back. You're simply in debt to your friend who had an extra $5 and who trusts you'll pay him back.
Now, let's say you purchase that happy meal using a credit card. Only a retard would say that the credit card company owns that happy meal until you pay them. (Hey, 6 hours later, it's in the sewer, you can have it back.) The credit card company trusts you to pay them back, based on your credit score. But they're not doing it because they're your friend, they're doing it to make a profit. The store pays them a little bit of money for their trouble, and if you don't pay within 30 days, you pay a small percentage in interest.
Now, let's say another company lends you a shitload of money. WAYYY more than $5. They trust you. But, they want to know exactly what you need that much money to purchase. They hope to make a small profit off the deal (in the form of charging you interest.) But, they're still not going to take as big of a risk - they attach strings to the loan - you have to purchase what it is that you said you're purchasing, and if you default on the loan, they get to have that thing instead, be it a car, or a house. It's a secured loan, which reduces their overall risk, because while they trust you, they still know that the future holds uncertainties. YOU own the house, but if you don't pay your debt, they have a legal contract that says that they can take possession of what you purchased with that loan so that they can use it to get their money back.
If you wanted to, and a credit card company was willing to risk that much money, you could purchase a house with a credit card & it would be an unsecured loan. (I.e. go to Detroit, put a $2000 house on a credit card, pay the closing costs with the credit card, etc.) If you default on the credit card, they don't get to take the house.
As far as taxes, yes, you own your home. As a home-owning member of society, you need to pay the government for services it provides to you, or decides to screw you over and provide those services elsewhere, like taking money from the blue states and providing it to the red states. However, like the bank, they've gamed the system where if you don't pay your share of services, they've (you have) given them the right to seize your property to sell in order to pay for those services.
I can't tell if you "you can't really own anything, you just rent it from the government" people are really loons who think that, or just joking.