For those who pay mortgages, this is not so easy a question. Maybe it could be argued that the Bank is also a co-owner. The common view on ownership has our hero Joe scraping together a lot of money, adding it to some money from a Bank, and trading this for a house.
Libertarians view ownership in much the same light.
If you buy a house, as long as you do not trespass or damage your neighbors' property, you should be able to do what you want. Libertarians feel that just as human rights allow you to live freely, and protect your body from interference, your property rights allow the same. But the Government's view on ownership is very different. In effect, even though Joe and his Bank traded a large sum of money for a plot of land, they really did not buy it. Joe only gave someone a lot of money to take over the rent of the land.