A couple of things:

1) I've always wondered what possessed Michael to tell her that story in the first place. That's a private, family story that implicates his father in crime - and he's telling it to an outsider? I get that she's his girlfriend...but still.

2) It was common in those days for Italians to hold great disdain for their sons marrying non-Italians. When my paternal grandparents (grandfather Italian, grandmother Irish) were dating in the late 1940s, his father used to refer to her as "Irish" - he would say, "Hey, Irish" when he saw her. When they got married in 1953, the women in the neighborhood came to my great grandmother - his mother - dressed in black and were pouring their sympathy to her - as if her son had died rather than gotten married. I can imagine Vito, as such, being even older than my great grandparents, probably thought his son an embarrassment for dating a non-Italian.