Kobe was 18 when he played against MJ for the first time. He told the story of trying to take away a screen play from Jordan, knowing what he wants to do, and MJ still doing it and dunking. Then in passing, MJ told Kobe, "A lot faster in person, isn't it?" That's when Kobe stopped being a fan and started to chase MJ. A chase he was on his entire career.
In 2003 Jordan announced he would retire from basketball (again). If Kobe was to prove he can take the torch, this was his last chance to do it mano a mano. In their first game, MJ and the Wizards got the better of Kobe and the Lakers. After the game, winning wasn't good enough for Jordan. He had to twist the knife. As told by Gilbert Arenas on the "No Chill Podcast," Kobe was wearing Air Jordan's at that game, and MJ used that to send a message.
“You could wear the shoes but never fill them”
Michael Jordan, No Chill Podcast
Kobe went full Mamba after that. As the story goes, he didn't speak to anyone for two weeks. Teammates got concerned that they did something wrong and went to Phil Jackson to find out what's going on. Phil told them it wasn't them and explained what MJ did at the end of the game. The team knew next time the Wizards came to town; it was going to be a show.
“They were like ‘I feel sorry for the next time we play Jordan’. They said they already knew what was gonna happen against MJ, when MJ came to L.A. Sure enough, Kobe went out and that motherf***er… He didn’t even have to tell the team. Once they heard what happened is what Kobe decided to do. Gave him 55!”
Gilbert Arenas, No Chill Podcast
Kobe was spectacular in that game: 15/29 from the field, 9/13 from the 3-point line, and was 16/18 from the free-throw line. Arenas weren't with the Wizards at that time, so we should take this story with a grain of salt. But knowing enough true stories about both parties involved, it fits the profile of both players.