I saw this snipet when researching THanksgiving with my school aged child for his project. Never knew the other side of this argument, other than infant baptism was abhorrant. So here's a start to my new understanding (others, feel free to add).
http://mayflowerhistory.com/religion/
Infant Baptism.
The Pilgrims believed baptism was the sacrament that wiped away Original Sin, and was a covenant with Christ and his chosen people (as circumcision had been to God and the Israelites), and therefore children should be baptized as infants. This was in opposition to the Anabaptists, who believed that baptism was essentially an initiation ceremony into the church-hood of believers, and therefore could only be administered to believing adults who understood the meaning of the ceremony. The Pilgrims, on the other hand, believed that "baptism now, as circumcision of old, is the seal of the covenant of God," and they felt that groups like the Anabaptists who did not baptize their infants were depriving Christ's flock of all its young lambs. Richard Clyfton, one of the founders of the Pilgrims' church, even published a book on the topic, A Plea For Infants (Amsterdam, 1610). They further believed that at least one parent must be of the faith for the child to be baptized into the church.