Should I move on or give him a second chance?

I was dating a man for a few months. Although it had only been a few months I really felt a connection with him. Honestly I fell in love. Ive been in a few relationships and Ive been in love before so its nothing new...its just been a while. We met on a dating site. We both agreed to be monogamous and to delete out accounts. Through a conversation I had with a male about how a lot of men not being trust worthy I decided to do a little checking around. I went back to the site that we met on and saw that his account was still active and he had updated his pictures. It said that he had been online that day. I confronted him and he said that he was up one night (he doesnt sleep well) and was bored. He said the site sent him an email notification and he just went on to check them because he was bored. And he said that he just updated his pictures because he was bored but did not make any contact with any other females. I of course did not believe him and called it off. It has been about a month and he has been after me non stop. He said that he swears on the life of his son that he is not lying about anything and nothing happened. My first problem is that he did not think anything of being on the site in the first place. I later learned that my profile was not deleted but you could clearly see that I had not been online...but that was not his reason for being online. His reason was that he was bored. Anyway, my second problem was that he updated his profile with pictures that I took of him. First he did not see why I was upset which was a big issue for me. Who would not know that being on a dating site and updating your profile is a no no?? He is 30 but seems to either be making childish mistakes or he is just lying. As I said he has been making pleas to get me back. He has started attending my church during a different service but I have started visiting another church. He came over and I met his son a few days ago. He said that he wants us to be a family. I said that if he thinks that was okay what else does he think is okay. A few people have said to give it a second chance because the relationship is so new that he might not have trusted that I really wanted something long term. But as a man shouldn't he have just asked? How do you tell a woman that you want to spend your life with her and then get bored and upload pictures to a dating site. I read some articles about men going online and checking out these sites as an ego boost. Sounds like an excuse to me...sounds like putting yourself in the way of temptation to me. Am I wrong? Am I overreacting? Should I chalk it up as a mistake? Or run?