People underestimating people is a major theme in the Trilogy. Barzini underestimated Michael. Michael knew it. That's why Barzini died, instead of Michael.
The reckoning between Michael and Barzini was inevitable. If Michael simply ducked the meeting, he wouldn't have resolved the basic problem: Barzini figuring him for a pushover, and encroaching on his territories. It had to happen.