Why do players dive for balls?

One thing that eludes me is why do players dive for balls at thier
opponent's end of the court? It seems like that would actually help
the other team more than yours.

a) you touch it but it still goes out so they get it back
b) you put it inbounds but they recover and now out man your team 5 -
4
c) Even if your team gets it back you're still outnumbered until you
get back in the game.

Yes I know a fast break can result from time to time but it dosen't
seem worth it considering all that can go wrong not to mention getting
hurt on such a dive.

Why not just let the ball go out of bounds and give your team
possession?