Median is what many people actually have in mind when they say "mean." It's easier to interpret the median: half the population is above this age and half are below. Mean is a little more subtle.
People look for symmetry and sometimes impose symmetry when it isn't there. The age distribution in a population is far from symmetric, so the mean could be misleading. Age distributions are something like a pyramid. Lots of children, not many elderly. (Or at least that's how it is in a sort of steady state. In the US, for example, the post-WWII baby boom generation has distorted the distribution as they age.)
With an asymmetrical distribution, it may be better to report the median because it is a symmetrical statistic in the sense that it splits the population in half. Said another way, the median is symmetrical even if the distribution isn't.
Update: I got my logic backward when I first answered and said the mean would be lower than the median. I meant the opposite.