As we pray in the Coptic version of the liturgy of St. Basil, "For no one is pure, if his life be but a day." We are born into a fallen world, even though we do not enter it guilty of anything.
There are also other reasons to baptize infants that don't really have to do with ancestral/original sin, such as the fact that this is the normative method of entering the Church community. Christ does say that unless we eat His flesh and drink His blood, we have no life in us, and so it would be a deprivation of life to not baptize them, since of course communion is restricted to baptized believers only.
This is one thing I absolutely don't get about some western Christians (and even non-Christians like Mormons, who I've learned fairly recently have a big hang-up on baptizing babies...kinda weird when you consider that they think of baptism as being so essential that they regularly 'baptize' dead people
); it seems to make the infant and the child into something less than full-fledged members of the Church. They're either in or they're not, right? It's very odd.