At the risk of not being kind to you...
Perhaps the thread would be better titled as "Why do women lie to themselves"
He told you he was living with someone, had kids with someone
He didn't tell you he was in an open relationship or that they practised ENM.
He told you that (at the very least) they were together for the kids.
he complimented me more and I started to fall for the attention. It felt good.
You knew he wasn't single.
Whether or not he and her were romantically entangled, a burgeoning relationship between you and him would represent a disruption to their child-raising partnership. In fact, if they truly are not romantically entangled, then you represent even more of a threat to that family stability.
He told you what you wanted to hear to get you into bed - it probably felt good to him to get affection and sex. So there's the answer to your original question.
But ask why did you lie to yourself? Was it similarly, just because it felt good??
If so, then there's not much difference between men and women when it comes to lying to get what you want.