Either we should baptize only believers or we should baptize believers and their babies. One of these must be right; the other must be wrong. One is old and apostolic; the other is newer. For the purpose of this paper, assume this much: The very early church practiced one teaching; the other developed later in the life of the church.
In the baptism debate, history seems unsatisfactory for two reasons. First, history is not clearly on either side of the debate. There were at least a few ancient Christians who seem to have practiced each baptismal system (or something near to it). And many old sources are vague enough that both sides claim them. Together, these mean that everyone comes away believing that they are in agreement with the vast majority of historical figures.