I think you’ve misunderstood what a mortgage is, you don’t own 10 percent of the house, you fully own and are the legal and only owner
a mortgage company takes a charge over the property, meaning they can take possession and force a sale if you default, but that does not make them the owner as you pay your mortgage (which is jist a loan) off
every month, assuming not an interest only mortgage, you pay off the capital sum, thus reducing what you owe, like any other loan. Bricks and mortar always increase in price over time, so your property gains in value over the period of the loan, as the capital sum outstanding decreases.
in rent, you pay to live in a property, like a hotel room, or air b n b. When you leave you have no right to the property, no increase in value, you’ve simply paid to stay there.
of course over time, owning and taking a loan to do so, is always financially preferential, but renting is a valid option should for whatever reason someone is able to buy and chooses not to.
But saying someone owns a small percentage is factually incorrect. They fully own 100 percent of the property and taking out a mortgage and having a charge over your property doesn’t change that.