In theory, you could build equity the first 10-20 years, once you hit 62 you could get a reverse mortgage (or other financing/home equity loan earlier than that) to tap into the equity to pay for living expenses (sort of an elaborate savings account/retirement plan). Also when calculating whether it's cheaper to buy vs. rent don't forget to factor in taxes - all the interest you pay on the mortgage is tax deductible. If you sell the house after 2 years, the capital gains from any increase in value are also not taxable. Mortgage payment will also stay constant, while rent generally increases (property taxes and insurance will likely go up though).

Plus you have the advantage of not giving all your money to subsidize landlords who are exploiting a basic human need - housing. If you have a decent landlord who keeps up with maintenance and doesn't ask for significant rent increases, it may be better to stay in your current situation.