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.
The Wikipedia article on the subject is very thorough.
Some of the reasons for doing it include:
Again, Wikipedia is helpful here.
It should be noted that many traditions that practice infant baptism have a secondary initiation, such as Confirmation, in which the person does get to "choose for themselves".
In the Methodist tradition, baptism of infants is a holy sacrament, welcoming the child into the church family and into God's grace.
It also involves a covenant by the parents and the congregation to teach and guide the child, to raise the child within a faith community, and to help lead the child to make a faith profession and become a disciple of Christ.
They don't "choose for themselves" because our sinful human nature does not give us the ability to make such a choice. We can only make that choice through the grace of God. The baptismal covenant is one way God imparts that grace to us.
The practice of baptizing one's children goes back to New Testament times (Acts 16:15, Acts 16:33). And baptism is analogous to circumcision (Colossians 2:11-13), which was practiced on infants as far back as Abraham's son Isaac.
If someone is older, and has not been baptized, and wishes to join the church, they can be baptized at that time. In fact, they must be baptized before making a profession of faith in front of the church, again to indicate that it is God's grace and not our own righteousness that enables us to make that profession.