"You're a kid" or "I'm older" is used for a few reasons:
1) They can't think of a better reason because they don't have any,
2) They can't think of a better reason because they can't explain it into words,
3) They can't be bothered to think of a better reason because they're lazy
4) They can't be bothered to think of a better reason because they think age/rank is authoritative and therefore the best reason.
I agree with everything Barles said.
I do not approve of the age card because it defaults a certain person's opinion as being right due to their age, rather than letting opinions be debated upon intellectual validity. In a technical argument (or rather, any argument in which you're trying to prove that you're right based on objective points), "Because I'm older" brings it down to subjectiveness inappropriately.
Where I do approve of its use is when the technical aspects of the argument have come to a standstill (ie grey zone), and the topic hinges on values and beliefs rather than straight logic or reason. As Barles has said, age "colours" the way you see things. In other words, your experiences and time spent alive can change your values and beliefs. What may be "worth it" when you're 20 years old may not be "worth it" any more when you're 40 years old.
That said, I "approve" of it being spoken about in order to give a perspective on the issue. It shouldn't be used to rule out younger thoughts on the matter. Because we're in the subjective region, someone else's changes after 10 years of living won't necessarily become your changes/realisations after 10 years. You lived in a different time, were possibly brought up differently and could very well experience things differently from each other during a 10 year period.
"Being older" can give a perspective or an anecdotal reference for someone who has not had as much exposure (either in the field you're talking about, or simply "being alive") to evaluate and think about, but should not be used to dictate that the younger person has to make one decision or another.
edit: How old are we talking about though En? Because biologically speaking, teenagers are still developing their pre-frontal cortex (which is used in decision making).