"If it's not man's responsibility to believe, then it makes no sense for Jesus to marvel at how much faith the centurion had or to marvel at the unbelief of the Nazarenes He was talking to. The faith someone had or lack thereof would never have surprised Jesus at all if faith was given to people rather than people using their God given free will to decide whether to believe or not."
References: 1) "When Jesus heard this, he marveled and said to those who followed him, “Truly, I tell you, with no one in Israel have I found such faith" (Matthew 8:10) and 2) "When Jesus heard these things, He marveled at him, and turning to the crowd that followed Him, said, “I tell you, not even in Israel have I found such faith" (Luke 7:9). Obviously, He was not previously oblivious to the fact that they had faith at all but rather a much greater faith ~ "such faith" ~ than any others even in Israel He had previously encountered. And, obviously, He said what He said there for the benefit of His hearers... including us.
Regarding His amazement at the unbelief of the Nazarenes in Mark 6, it is similar, in the sense that even though He "laid his hands on a few sick people and healed them" ~ gave them signs to believe, they still did not. Again, the obvious comparison is in relation to others... His amazement was not merely that they did not believe but that their unbelief was stronger than others He had encountered.
Finally, this belief is not a responsibility, it is an ability... and an act of the will. Our responsibility, as Christians, is to love God (first, of course, and above all) and to love our neighbor as ourselves. And this love is far, far more than just a warm fuzzy feeling, it is a call to action. 'Responsibility'... You know this: the root word of 'responsibility' is 'respond.' In doing these things... and this is a rhetorical question, really... what are we responding to? <smile> Remember what John says: "We love because He first loved us" (1 John 4:19). <smile> And then... and this brings us back to the topic being discussed... why? What is it in us, that is now in us that was not there before, that causes us to respond in that way? <smile> Hint: It starts with an 'h.' And/or an 's.' And either way, it is put into us by God. <smile>
Grace and peace to all.