"The Church received from the apostles the tradition of giving baptism even to infants. The apostles, to whom were committed the secrets of the divine sacraments, knew there are in everyone innate strains of [original] sin, which must be washed away through water and the Spirit" (Commentaries on Romans 5:9 [A.D. 248]).
I would say the error of infant baptism came about because of another error known as 'original sin', neither of which the apostles taught yet Catholics and some non-Catholics believe in anyway. The purpose of baptism is 'for the remission of sins" Acts 2:38 yet infants have no sins to be remitted. Jesus, speaking of children, said "for such are the kingdom of heaven" Mt 19. The kingdom of heaven is not made up of lost, unforgiven reprobates. Also in Mk 16:16 Jesus made belief a prerequisite to baptism. Infants have not developed the intellectual ability to hear and believe as the bible requires, infants have no language skills to understand gospel words being spoken.
It is sometimes argued in Acts 16:30-33 infants were baptized. It is "assumed" infants were in the house. It is also said the word of the Lord was spoke to all that were in the jailer's house, v32. Again, infants have no language skills or the cognitive development necessary to understand the words being spoken. Anyone, infant or adult, that does not believe, does not understand the gospel words are NOT candidates for baptism. Those so called "church fathers" contradicted the bible, and each other, on various issues.