Should he be messaging another girl on social media?

I caught boyfriend of 2 years who we have just bought our first home together messaging another girl on social media:
He went for a night out with some friends Saturday then on Monday I came across some messages with a girl asking about his friend he was with that night. He asks her for her friends account and suggests they should all go for drinks.
As far as I'm aware he has not spoke to the other girl which he asked about.
I have confronted it about him and he claims it was small talk. He switches from saying he was wrong to he can't see what he has done wrong but understands I'm hurt.
Am I over reacting?
Should he be messaging another girl on social media?
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