Boyfriend wants to cheat??

Me (22) and my boyfriend (25) are expecting our rainbow baby in August 2022. We had some relationship problems and broke up briefly last year. I found out he cheated (was just a kiss but not the point) and when we split, I briefly dated someone who I decided was not for me about 2 weeks in although we were broken up, he called me a cheater, liar etc I didn’t hide the fact I was dating from him. This was around August/September after we lost our last baby. I thought we had both managed to move forward, we communicated a lot and reconnected with one another. It was difficult for both of us, but I honestly thought we were stronger than ever after this. We spent a lot of time working on ourselves and taking time apart but also reconnecting as a couple. Don’t get me wrong this baby wasn’t planned but we were both aware it was a possibility and were overjoyed when we found out. We currently don’t share a home, but he stays at my flat most nights, pretty much consistently. We have put a deposit down for a new build as we want to have a fresh start and a new house for the baby coming and planned on getting married so that we can share his name as a family. As nothing about the past issues has been discussed recently, I was shocked when yesterday he said to me, he thinks he should sleep with someone else before we move into the new house. Because he feels it’s the only way, we will be able to move forward with our relationship. I was shocked and taken back by this as I don’t know how he can even think about that when we have a baby on the way, I honestly didn’t know what to say. He said if he didn’t do it now, he wouldn’t be able to once the baby was here. He claims its not even about the sex but that he feels things are unfair and un-level between us, which while maybe true in his opinion but I feel that it’s just very concerning that he can even think about sex with someone other than me in general let alone while I’m pregnant, I am a high-risk pregnancy and trying to be calm about this and not stress. He has constantly reassured me that he loves me so much since this conversation, but I just don’t see how this can be true when I know he feels like he wants to cheat. Less than 12 hours after this conversation I seen he was hiding his phone and there was a visible message to another female and probably others I didn’t see. So clearly already seeking people out which is making me sick. I didn’t bring it up as he knew I seen it. He says there’s a 60% chance he won’t do it as if that would make me feel any better!!

I don’t really know where this leaves our relationship. I’m thankful he has been honest and told me he is feeling like this but if he does cheat, I don’t think I will be able to forgive him or move forward. It will ruin my pregnancy as it will become the focus. I know he will be a great dad regardless of whether we are together or not but as the baby’s father I don’t know why he would want to treat me badly when I am growing his child. Should I leave or try to work through this providing he doesn’t actually cheat? Any advise or similar situations welcome, also please don’t be worried about offending – what he has said is the most offensive.