Instead, he came to love Bryant as the little brother he never had, and as a student eager to learn from Jordan's experiences and skills.
"He wanted to be the best basketball player that he could be," Jordan said Monday at Bryant's public memorial service at Staples Center. "And as I got to know him, I wanted to be the best big brother that I could be."
Jordan broke into tears with those words during a moving speech about his largely unpublicized friendship with Bryant, who died along with his 13-year-old daughter, Gianna, and seven others in a helicopter crash Jan. 26.
"When Kobe Bryant died, a piece of me died," Jordan said. "And as I look (around) this arena and across the globe, a piece of you died, or else you wouldn't be here. Those are the memories that we have to live with and we learn from. I promise you from this day forward, I will live with the memories of knowing that little brother that I tried to help in every way I could. Please rest in peace, little brother."
The heartfelt comments from Jordan, the relatively media-shy billionaire owner of the Charlotte Hornets, were a poignant highlight of the two-hour ceremony. Jordan also provided a memorable image from the event when he stepped up to help Vanessa Bryant off the stage after she delivered her eulogy of her husband and daughter.
Bryant's career with the Los Angeles Lakers took off in the late 1990s when Jordan was wrapping up his own stellar career with the Chicago Bulls. The two shooting guards with silky, aggressive offensive games competed fiercely against each other, with Jordan initially unwilling to cede ground to Bryant as the next superstar at their position.
But once they became acquaintances, Bryant bombarded Jordan with late-night phone calls and questions about how to improve. When a retired Jordan traveled to Los Angeles to visit Phil Jackson, the former Bulls coach then in charge of the Lakers, Jordan was greeted by Bryant — who immediately asked him if he had brought his shoes so they could play.
"No matter where he saw me, he saw the challenge," Jordan said. "And I admired him because of his passion. You rarely see someone who's looking and trying to improve each and every day, not just in sports, but as a parent, as a husband. I am inspired by what he's done and what he's shared with Vanessa, and what he's shared with his kids."
Bryant kept up his questions even during their retirements. Just a couple of months ago, Bryant texted Jordan for insight on teaching moves to Gigi Bryant, who aspired to a basketball career.
Jordan is the fifth-leading scorer in NBA history with 32,292 points. Bryant — who played 274 more games — passed him on the career scoring list during his penultimate season in December 2014.
Kobe's 33,643 points currently put him fourth on the chart, with only Kareem Abdul-Jabbar, Karl Malone and LeBron James above them.
Jordan won six titles with the Bulls, while Bryant won five rings and reached seven NBA Finals with the Lakers.
Fans have spent decades comparing Jordan to Bryant, and comparing both to James. Jordan isn't interested in that game.
"Kobe never left anything on the court, and I think that's what he would want for us to do," Jordan said. "No one knows how much time we have. That's why we must live in the moment. We must enjoy the moment. We must reach and see and spend as much time as we can with our families and friends and the people that we absolutely love."
Jordan teared up several times during his speech, which allowed him to bring a moment of levity to the somber proceedings.
He is well aware of the Crying Jordan meme in which an Associated Press photo of his tear-stained face from his 2009 Basketball Hall of Fame induction ceremony is superimposed on athletes and public figures at moments of loss or disappointment.
"Now he's got me. I'm going to have to look at another crying meme for the next ..." Jordan said while the arena dissolved into laughter.
"I told my wife I wasn't going to do this because I didn't want to see that for the next three or four years," Jordan added. "That is what Kobe Bryant does to me. I'm pretty sure Vanessa and his friends all can say the same thing. He knows how to get to you in a way that affects you personally. Even though if he's being a pain in the ass, you have a sense of love for him and the way that he can bring out the best in you, and he did that for me."