An Hee Tae wrote:A:Look at the guy with hat!
He has been after me. He came on too strong.
B:Oh,he's good looking.
Why not going out with him?
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'http://www.stoo.com/html/stooview/2004/0707/091991140412191215.html'
'Have been after me' means the other sex chase me from past to now.
And, 'come on too strong' means someone do greatly effort for getting some things.
I don't know why stoo.com used "why not going..." I've never heard why not + -ing. This should be Why not go out with him? - why not + base verb. It's a bit more casual than "Why don't you go out with him?" but the meaning is the same.