LlamaLarry has made some valid points. I think the arguments about too expensive, too robust (???) too flash, too posh etc etc, are all too vague and don't make any valid points.
Questions you should be looking for an answer to are:
1. Is money of concern (ie, what value are you willing to spend on your 13 yr old child)?
2. Is the child responsible enough to look after it and respect it?
3. What is the purpose of the laptop now, and in the future?
4. How long do you plan to have this laptop working for your child/children?
My Things 2 & 3 have been 'given' iPads at school as a lot of material and notes are now distributed by PDF. They are 12 & 8 respectively.
All mine have had access to a iMac for about 5 years now so in theory, Thing 4 (I like your analogy LlamaLarry) would have been only 2 when they first had access to a computer.
HOWEVER ----- I use Apple Parental Control on everything. I lock down internet access to whitelist sites for all users except myself and my wife. No PC use outside of common areas. No Facebook/twitter/youtube for anyone (even now with older kids)... I have managed to convince all my kids that Facebook is evil and corrupt


I don't use it on Apple but K9 Web Protection is very good on a Windows PC and is now available on mac an IOS as well.
Yes, I would recommend a MBA (or any other Mac laptop) for your 13 year old. New or 2nd hand is a financial consideration only you can answer. I tend to go for 2nd hand for the kids (ie, my old hand-me-downs) but that is the benefit of Apple laptops. We are still rocking a 2006 iMac and it is running Lion and works really well for Web, email and small word/XL stuff for the kids. They do last a long time if looked after!