Why do older students take longer to learn to fly?
This question is more related to human aging and learning than it is to aviation. When people age, there is a toll on several parts of body and the acquired skills may not stay as sharp as they used to be.

As we age, learning new things become harder, not because we are getting stupid, but because learning new things is intrinsically hard. Almost all people get into a profession in their early 20s, but it becomes harder to change their career later in life. The reason is that they have more things on their mind to worry about as opposed to the early phases of life.

One does not stay young forever. And you cannot point out one or two or ten things which makes learning new things hard. It is a combination of many factors. That being said, becoming a pilot in your 50s or 60s is harder than in your 20s or 30s, but there are many old pilots who can do and have done things which younger ones cannot do. Example: Captain Sully

You can ask why most athletes are in their 20s, not in their 60s, and will get a similar answer.