He’s not showing you because his PRIMARY concern is you leaving him and this will upset him. Because he thought in his life he could have his cake and eat it. He wants to remain in control of the situation. He wants you to provide 80% and the missing 20% he thinks he deserves to get elsewhere. ‘Woe is me you never text me ego kibbles so I deserve them from Janet’.
When you see the messages you may leave. He cares about him. Selfish just like when he was getting his ego kibbles via his phone.
Showing you the messages means you will see who he is and what he was prepared to do to get his ego massaged. He wants to hide this from you.
Read the book ‘not just friends’ by Shirley Glass. He has opened the door to this nonsense. He is not showing you to protect himself and remain in control of the situation. If protecting you was his primary concern he wouldn’t have done it.
He is a typical cheat that doesn’t want to be honest and face the music - they are 10 a penny. We only text, we only touched hands, we only kissed once, she only gave me oral, we only had sex once, three times, 10 times, I didn’t enjoy it, etc. He may never have met up with her - it’s a shame he can’t show you the messages to help evidence that it meant nothing.
Cheats are boringly predicatable. They care about themselves and how they feel.
He is a cheat who is sad he was caught. He doesn’t want to give you the full information as he doesn’t think you deserve to make an informed decision about whether you want to stay with him. That is who he is.