Bf/Bd always lies

My bf has always had issues with lying. Even if it’s little things. A couple days ago he lied to me about something very serious. It took me 8 hrs to get the truth out of him and I still dk if it’s the full truth. Today he was on the game and told me an hour ago that that was his last game and that he will take our 2 yr old a bath. An hour later I question him about it and he tried to lie and say that he was still on the same round that it didn’t finish. It took me a minute to convince him I’m not a dumbass ik how COD works and for him to admit he lied. He’s mad at me for being mad now.

Is this something you’d leave ur bd over ? Or am I overreacting?