Disapproving parents

The man I'm currently dating is 27, I'm almost 26. My parents met him the first time a few nights ago and loved him until my dad dug up his past. When he was 19 he was with a girl who lied about her age and wasn't actually legal consent age.. her parents pressed charges and he has a change or corruption of a minor, meaning he's technically a sex offender. I know the story, so I understand and it was a long time ago. My dad can't get over it though, which I understand to a point. He won't listen to what happened though and I'm torn. This guy and I are doing very well together and we both just clicked, but I've always been daddy's little girl and my family's approval means a lot to me. I'm not sure what to do, has anyone been in a situation like this or have any advice on what they would do?