I think what your friend meant is that at a younger age, your muscles and joints are more flexible.
This just makes it easier to increase and maintain that flexibility for martial arts such as TKD.
As you get older, it becomes harder to stretch those muscles and ligaments.

I could do the splits when I was much younger, so when I started TKD, kicking high wasn't really a problem.
However, I tried doing the splits again and it....hurt. I doubt any kicks of mine can hit the head of a person with similar height now. lol

But that's just for sport.
You can learn martial arts at any age. To learn the techniques and art behind it, and enough for self-defense.
Don't start learning a martial art just because you 'want to know how to fight'. That's only going to get you hurt.