breakup or...?

I gave my boyfriend multiple chances to stop texting a so-called “friend” but he won’t stop. and every time I ask him about it he lies. Should i break up with him? i don’t like him texting other

females because he come off as too friendly and i spoke to him about this multiple times. it hurt me deeply. but when i try to break up with him something always hold me back. we’ve been together for 3 years. what should i do?

Edit:

our relationship rule is that we don’t text anyone of the opposite sex.

i don’t like for him to text this girl impartial because he seems to me they like each other