I agree.
Here's why I think people consider age important:
We like to compare ourselves to other people. When we see little kids performing something we can't, it either motivates or depresses us. We want to be the best in every aspect and when we see that we are not, we push more until we are.
I just think that the previous goes not only for myself, but at least some other people as well - that's why I used plural in the sentences.
I'm constantly trying to make it clear to myself that comparing people doesn't make any sense - people are way too different to compare. We differ by our goals, abilities, character and so on and because of that, we can't compare ourselves by our abilities or by the properties of our characters. Nobody is better than anyone else already because the word "better" implies that the two objects can somehow be measured.
For some reason, I never seem to actually get it - I know that I can't compare myself to others, but I'm still doing it and I still feel bad if I see that I have gotten a grade even worse than a few of my classmates.