When Michael is walking with his kids, he tells Mary that she cannot be associated with Vincent in "that fashion" and that Vincent is her first cousin. He is clearly concerned as any father would be about the sanguinary and moral implications of such a relationship. beyond that you can impute other concerns of him.

"Generosity. That was my first mistake."
"Experience must be our only guide; reason may mislead us."
"Instagram is Twitter for people who can't read."