Should I leave him B/c of FACEBOOK? What do you think?

Ok I don't know if this is a stupid reason to break up with him,but here it goes.... I been with my fiance for 7 yrs and we have a lil girl together... Well the other day i was going through my facebook page and a friend of my commented on my status and so i commented back and went to veiw her profile.... well I saw that my fieance had a page well i asn't upset b/c he did tell me he had one but the thing that upset me is that he did not ask me to be a friend but he went out of his way to look for her...(shes a good looking girl) I'm not upset that he ha a facebook page but upset that hes had his page for 2 months and never looked me up and had time to ask my friend to be his friend... whats up with that?? And when i asked him he said he dosen't even go on there or has time to look for friends... Which he is lying bc i've looked at his page and hes been on almost every day... I called her and she told me he requested her and on his realtionship statues he has nothing...I hate that he lied to me... what should i do... ???