... during the conversation, Michael's demeanor changes and he ends up taking Vincent under his wing. Why? What does Vincent say or do in that scene that impresses Michael so much?
It's called 'lousy writing', and it's the front & foremost reason for GFIII being so inferior to the other two.
Apple
A wise and frugal government, which shall leave men free to regulate their own pursuits of industry and improvement, and shall not take from the mouth of labor the bread it has earned - this is the sum of good government.
