Well, he might be a liar, but it takes a lot of guts to tell a woman he has misbehaved in such way. He certainly cares about you enough to come upfront with the truth.
Having said that, I once dated someone who told me he had a friend who he had sex with after a drunken night, and that they had accidentally fallen pregnant, but that he told her that although he couldn't start a serious relationship with her because of the pregnancy, that he would support the baby if she decided to go ahead with the pregnancy. He also told me that when she decided to have a termination, he was with her, paid for the procedure and was there holding her hand for most of the process. ah, and that someone will come eventually to tell me about it.
... and so they did, so I realised that all the above where half truths, he had been chasing the woman for ages but she was not really that convinced of having a serious relationship with him. They fell pregnant after weeks of sex for the sex sake and when she decided to have a termination, he took her to the clinic, pay for the cheapest and most traumatic procedure, took her back home and... NEVER ever called her again or pick up the phone when she called him.
The former I have no problem with, the later... was a deal breaker.
So... do your research before you get attached to this man.