AM I right to end the relationship?

So I just broke up with my boyfriend of 4 months. Not a long relationship but I just want to know for future reference if I was right. It all started when I was sitting at his house watching a baseball game with him and his dad and the whole time he's ignoring me and texting someone (not a normal behavior of his, he rarely texts) so I look over and see its his ex-girlfriend. Weird. I get upset and leave. not like overreacting but just aggravated. I forgive him tell him to stop nicely. he says he's going to delete her number and never talk to her again.. blah blah blah.. he doesn't. they continue talking for a week daily (he didn't tell me I found out later when I looked through his messages). they dated about a year ago for two year mind you. I asked him again to stop. I decided to snoop into these conversations. first one was him saying how I hate him (totally dont) and he wants to see her. the next day he's texting about how they hung out on friday .. he didn't tell me that he about it obviously. and also about how he cares about her and doesn't want to leave me because she won't leave her boyfriend. I didn't tell him I read them but asked him if anything was going on between them I should know about. he said no they only talked that one day we watched the game together. I asked I'm a few times and said the relationship is done if he doesn't fess up. so I break up with him. later that day I fess to reading his phone and knowing they hung out. he says they had lunch to discuss how much he loves me and how he's over her. obviously something that should've been established a while ago then I knew it was done. but was I right to think that something was up?
AM I right to end the relationship?
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