Because it is his special power, one which was never seen before in the Naruto Universe... the power to change people's hearts, to make them believe in him... a very interesting power indeed, which he managed to harness it through his Talk no Jutsu.
Also Minato and Kushina believe in him cause he's their kid, and as said by Minato, parents always believe in their children no matter what. Also Kakashi an Jyraia are his teachers so they also have to believe in him.
Also his ninja way "to never give up" comes in handy as well, cause if you doubt him, he won't stop until he proves you wrong.