Don't. He's trying to scam you.
lol. Not necessarily.
There is an Apple website that you can use to check warranties. I've seen serial numbers exchanged before solely for this purpose.
There is very little he can do with the serial number. Maybe try to move the device over into his support profile, but I'm not sure what he could do with that besides see what the device's service history is.
For everyone saying it is a scam or dangerous, what can they do with the serial number?
Personally, I would not do it, just to be safe, unless he has a good feedback rating and is serious about the purchase. But I cannot think of any specific danger in doing so. Maybe except for him using it to give to other people while trying to scam them (i.e. using your serial number for when they run warranty checks).