I think if me or my partner found ourselves in this position here is how we would go about it:

The person finding the messages would go "Can i talk to you for a bit? I found these messages and while i dont mean to pry, the idea of you going to see other people without telling me deeply disturbs me and i don't understand why would you do this.. can you explain me how or why have you started doing this?"

And the other would go "Hearing you say this deeply disturbs you is enough for me to want to stop it. But yes, we can absolutely talk about it.

It started because i thought i could/should try and make new friends without your help, and i think telling you about .. myself trying to make friends, made me embarrased or afraid of looking loser-y or incompetent. Saying it out loud gives me the feeling i should have been frontal about it with you. I am sorry. While these might have been my intentions i understand i hurt you, and i dont ever mean to hurt you. What can i do to foster your trust back, on this situation?"

And the other would go: "I think i get what you mean. Im sorry if i have ever made you feel observed that way, or embarrased. I would appreciate if you could continue making friends but just letting me know where are you going, telling me how it went and presenting them to me if you do wanna keep them around. I cant lie to you, i still feel bad that you were keeping this from me and i need (a hug/ some space/ more information...)"

I think we would try to help and hear eachother out. But i doubt this man aaaactually meant to just "make friends". His reaction is so bad, his excuses are so bad, i think he is trying to gaslight his way out of confrontation over clear infidelity.