What traditions espouse infant baptism and why? What traditions espouse infant baptism and why?

In those traditions, why do parents often baptize their children at very young age, and why is this better than giving their children the opportunity to choose for themselves?
At least the Roman Catholic and Presbyterian churches do. A fairly comprehensive list is available on the wikipedia article.

As to the why, at least from the Presbyterian perspective, children of saints are viewed as being born into a covenantal relationship in similar vein to the males of ancient Israel being required to be circumcised.

Fuller paedobaptist theology is also covered on the wikipedia page.