Because when you are 70 years or older your cognitive abilities are not what they used to be.

Would you want a 70 year old person to be trained as a fighter pilot? Would you want him or her as a fireman, trying to carry people out of a fire?

A lot of great people are sharp and intelligent far into their old age, and a lot more people are not. But their brain doesnt learn as fast, doesnt adapt as well.

I want the person sitting on the nuclear button, who decides our climate policy, that decides about health care, about using our military, to be in their prime.

There are reasons for mandatory limits in certain professions, having one for becoming president is a good idea.

A lot of decision making is made by staffers. They rely on staffers to due the heavy lifting, and then the elected public official goes through the motion of reading statements written by staffers, introducing legislation, etc. Parliamentarians are quite important to Congress' day-to-day functioning. Also, as a public official, your party's platform already outlines what sides of issues you are on.

"Would you want a 70 year old person to be trained as a fighter pilot? Would you want him or her as a fireman, trying to carry people out of a fire?"

No, but those aren't the jobs under consideration here. The President can usually check with advisors and take five minutes or a couple of weeks to work out a response. "Nuclear button" is the only one of the items listed that would be a five-minute response; policies can easily wait a week or more to work out. How long did it take to put the ACA together?

Life expectancy and health (mental & physical) matters. Especially in the case of a President. Plus you want them to be able to serve 2 terms, so you need to consider current age + 8 years.

Age related cognitive decline is a real thing.