Business, I'm guessing. I think that betrayal was never far from Vito's realm of possibilities--comes with the territory. Attest his policy of giving orders to one person at a time, or through Tim, to prevent a corroborating witness who could testify against him. I think he also advised Michael to have everyone's phones tapped or monitored. Mostly, I think he'd be rightly suspicious that Michael wouldn't be accepted as his successor--he'd see that as business, not personal to him.
Nice to see you again, DT!