Is it wrong not to trust him?

My guy and I have been together for a year this month. We met on the internet. It wasn't a dating website just a social one. About two to three months after we first met on that website I found out that he was sweet talking another girl on the site at the same time he had been talking to me. Ever since I found that out I have had some trust issues. Whenever we go out somewhere and I catch him looking at a pretty girl, I get so hurt and upset about it. I didn't say anything to him until recently about the issues I was having and he dismissed it saying it was ridiculous to even think that he'd ever want any other girl but me. I don't think he'd ever cheat on me but, to me, even staring at another girl is wrong. It might be good to get some guys' perspective on this. Do you think I'm wrong for doubting my boyfriend?