Unlike other celebrities (actors come to mind), professional athletes spend much of their time traveling. They become connoisseurs in getting from place to place, and the fact that they prefer private jets is telling. This is a travel tidbit everyone could pickup.
There are a number of reasons that pro athletes utilize private aircraft to travel.
Performance. Pro athletes have to arrive in the best shape that they can. Many times they may be performing within hours of landing. That means they have to arrive well rested, limber, and stress free. Private jets have more room to stretch, privacy to remove any stresses, and are a luxurious time while in transit. This is opposed to any other mode of travel, like the commercial airlines, which would be nothing but stressed for long periods of time in cramped spaces.
Privacy. Though sport stars are athletes, they are also celebrities. This means that they have to deal with crowds and fans, and would like to limit their exposure until game time. Flying aboard a private aircraft they get to have their schedule kept private (when they leave and arrive). Athletes also get to leave from private hangars and terminals so there are no crowds to contend with. They simply have to get to the airport and then leave, no getting there hours ahead of time for security and check-in. Then, when in the air they are only traveling with people they know.
Size. When traveling as a team, size matters. There needs to be plenty of room for everyone. Only a private aircraft can offer that with business class seating throughout the aircraft. Consider that most athletes are going to be physically larger, in a good way, than most people, room is important.
Also consider, that many professional athletes travel a lot during off-season also. For that the above still applies but it also means that a smaller private aircraft, yet just as well appointed, is needed. A few professional athletes can afford the long term expense of private jet ownership, but for many it means flying aboard a private charter. A private charter can take a single athlete from one location to another in a smaller aircraft where they still can enjoy all the benefits previously mentioned. Still, a charter will be much cheaper than ownership. The upside is that flying like a professional athlete with all the benefits can be accessible to everyone.