The respect between Kobe Bryant and Michael Jordan was huge. They considered each other a brother due to all the similarities in their personalities, games and the way they approached the game. It was so huge that they believed nobody could beat them 1-on-1 except for them.
It's curious, but that's what they thought. Ahead of the launch of NBA 2K14, MJ was interviewed by 2K and he revealed some details about his trash-talking game and his former opponents. At some point, Jordan was asked who he wanted to play 1-on-1, as to what he replied (3.30 minute mark):
"The list is too long, start off with Jerry West, Elgin Baylor, Kobe Bryant in his prime, LeBron in his prime, D-Wade in his prime, Melo, that's a good start. I don't think I would lose, other than Kobe Bryant because he steals all my moves."
Two years later, during a press conference, Kobe Bryant was asked if anybody had beaten him 1-on-1. Truth to his style, Kobe replied, leaving no doubt that only one guy can take him and defeat him 1-on-1.
"If there was going to be a player who could beat me, he retired after the last shot in Utah 98."
These two enjoyed going one-on-one with his rivals. They lived for it and they were the best at it. It would've been interesting to see KB24 going against MJ while both were in their primes but that's not how things work. Still, they pay their due respect to each other. MJ was well aware that Kobe could do anything he does and Kobe knew that his mentor was the one who could take him down.
Game recognizes game, especially when it comes to Kobe and Jordan.