would you leave or give a 2nd chance?

I recently caught my boyfriend of 2.5 years talking to a few girls on his Instagram. All were from girls HE MESSAGED that he claims he knows. One of the girls wrote some heart face emojis while he wrote nothing inappropriate back he STILL continued the convo with her, one he was just talking to about life but not really mentioning me, and the other he just asked how they were (and he wasn’t even following them) He never told me about these messages and when I asked if he’s talked to anyone he lied to me. So he lied and messaged females behind my back. I feel so shocked because I really trusted him. He’s the first to really get close to my family and I feel pretty hurt and betrayed and stupid. I’m pretty sure there’s been more behind my back, but I will never know. I’m so lost and confused. I asked if he would care if he was in my shoes and he said yes. Would you give a second chance? How can I trust him again that he won’t betray me. Or would you leave him?

Update: Now he is saying he will delete Instagram and disconnect his phone to prove to me whatever he can so he doesn’t lose me.