Do you want to redecorate to your own taste?
Can you even find anywhere to rent? Not everywhere has a liquid rental market.
Moving only once every 10 years sounds great. Renting means maybe having to move on notice as short as one month. Back when I was renting I moved about every 3 years, although that was also house-sharing with other young professionals.
Rent is usually more expensive than mortgage payments, and house price appreciation is your only chance to make a leveraged investment that pays roughly 7% annually.
Edit: also, obviously, after 20 years you have no more payments. Frees up a whole lot of cashflow. Would you really want to go into retirement on a fixed income with a variable rent payment?
Note that a "20 year mortgage" just sets the amortisation rate of the payments; you can accelerate it, and usually will end up re-mortgaging every 3-5 years to get better rates.