As a child, your first game of basketball is a world of discovery. As you are not allowed to run with the ball it is important to learn to dribble it, and this is something that plays a very important part in the smooth running of the game. Many novice players, aware that they have to keep bouncing the ball, will feel more comfortable doing so with both hands. Once you are in a league game, though, this is actually against the rules, giving as it does an unfair advantage to the team in possession.
The “Double Dribble” rule is one of basketball’s more esoteric ones, and is rarely seen in action in the NBA due to the tactical importance of retaining possession until you are in position to score. The most common infraction under the double dribble rule is when a player comes to a stop and takes the ball in both hands before looking around for a pass, and continuing to dribble if they see no options. Once you have stopped still to look around, it is obligatory to either attempt a shot or pass the ball to a team mate.
The reason that this is so important is that carrying the ball is illegal, and stopping with the ball in both hands is a clear effort to retain the ball without the risk of an opponent taking hold of it. In basketball, the continued recycling of possession is an important part of the game, and for a player to effectively carry the ball with him is an unfair excessive protection of the ball.