Would a guy be so adamant and swear up and down something not true even if he was lying about it?

Anonymous
So basically I have a iPhone and it adds people in my contacts to messenger on Facebook. Well it added this guy I’m talking to and his profile was no profile picture and 6 friends. I investigated more & found his relatives which let me to possibly to a profile of his sons baby momma. He has a three year old son. Anyways on HER Facebook it says engaged December 2018 to this guy I’m talking to & in bio it says to be married October 2020. It has a relationship link to his profile which has a profile picture and also says engaged to this women. I confronted him about it when he called me yesterday morning. He could tell something was wrong. I told him don’t worry about it. He kept pushing and was getting mad I wouldn’t tell him so I said fine. But yourll probably stop talking to me. He said I like you you would have to do something extremely bad for me to not talk to you. I said so are you secretly engaged or married and talking to me? He said what? No I’m not. I said you promise! He said yes I promise! So I went to work and all day I couldn’t get it out of my head. Me and him were texting eachother all day because we both were at work. So on my break he called me again and I asked again and he said I already told u no I I’m not gonna cheat on you! I said no I’m asking if your already in a relationship and engaged while talking to me. He swore up and down on the phone he’s not and would get mad because I kept bringing it up. So later last night he asked if we could FaceTime. We did and I asked again and he said no! He admitted he was engaged to baby momma a few years ago but she was drama so there not together, not on good terms because she gives him issues to see his kid. He also said he hasn’t been on fb in awhile

BUT when I go on Facebook and snoop I see otherwise. both their profiles say engaged to eachother and his profile of the three of them hers is him and her. If I go on his parents fb I see posts of them from June Father’s Day and she’s tagged in stuff.
Updates:
7 mo
PLEASE READ*

So I’ve talked to a guy before who was secretly still married and claimed he was divorced and wife cheated on him and I ended up finding out on Facebook that wasn’t true and I sent his supposedly ex wife a fb message and asked her nicely is she married to him is this her husband? Turns out he lied about everything and made shit up (Town he lives in, his phone number, lies about his wife cheating, and # of kids he has) So I told this guy about it and told him first day we talked
7 mo
I have trust issues and he said me too because the women he was with for 7 years cheated on him with co worker (And now I’m assuming it was possibly baby momma)

So would a guy go through this much trouble if he was lieing? What should I do?
Would a guy be so adamant and swear up and down something not true even if he was lying about it?
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