"Maybe by psychology it was not easy for Kasparov to face his student"
Kasparov also always talked a lot about destiny, and that some players were destined to win the title while others, like Bronstein and Korchnoi, were destined not to. He also said that Kramnik was going to succeed him, and then it almost looks as if he turned it into a self-fulfilling prophecy by giving him that title match. But these things can also be inexplicable, difficult to see why for example Tal always did horribly against Polugaevsky.
If Carlsen plays like Carlsen and not like Kasparov then I think Carlsen would have a good chance to win the match they would play.