Most Helpful Guy
It's totally okay for you to want your boyfriend to not flirt with other girls.
You have to tell him that you have a problem with it though. If he doesn't know you don't like it (and he doesn't unless you've *told* him) then you have no right to get mad.
Most Helpful Girl
It just seems odd. He's with you, why flirt with other girls? It seems disrespectful to me. I don't think you are being irrational or possessive at all. If anything it seems pretty natural to be bothered a bit by the behaviour.
I would talk to him. Some people are definitely more flirty, but he also needs to respect your feelings.