One reason is cost. When you're having to produce so many basketballs, finding a cheaper way to do it would make sense.
From the eHow article on basketballs (emphasis mine):
Balls that are 100 percent genuine leather are the best ones available and are used in the NBA and WNBA. Leather balls develop a broken-in feel after repeated use. This type of leather basketball should only be used on indoor courts. It is also the most expensive type of ball to purchase because it is made of genuine leather.
Synthetic or composite leather is an artificial type of material that feels like leather but is cheaper to produce. The materials are also more versatile and can be used both indoors and outdoors. Synthetic leather doesn't need to be broken in as it already has that softer feeling to it.
From Wikipedia (emphasis mine):
Balls are generally designated for indoor (generally made of leather or absorbent composites), or all-surface use (generally made of rubber or durable composites, also known as Indoor/Outdoor balls). Indoor balls tend to be considerably more expensive than all-surface balls due to cost of materials.
Through these clips, we can also see that composite balls are more durable, especially for outdoor use, which really shouldn't matter in the NBA. Their longevity compared to leather balls would also help reduce costs since replacements wouldn't be needed as frequently.
Another reason is quality. Straight from NBA.com in 2006:
The material is a microfiber composite with moisture management that provides superior grip and feel throughout the course of a game. Additionally, the new composite material eliminates the need for a break-in period, which is necessary for the current leather ball, and achieves consistency from ball to ball.
The players disagreed with the first point made here, causing the league to revert back to leather balls. With how hard NBA players pass and shoot, it is possible that the "superior grip and feel" translated to a rougher ball that caused small cuts.
The consistency between balls without breaking them in is an improvement that theoretically would provide a more level playing field for teams. Having better consistency would reduce the number of variables that could impact game outcomes. This seems minor and relatively silly, but the league wants to ensure the only variables between games is how well a team plays; any reduction in variability outside of team skill would try to be controlled.