Are infants not children? Tell me, how old were the children? When does an infant stop being an infant and become a child? The word translated as "little children" is
paidion. This word means "a little child, an infant, little one." Aristophanes says the first three stages of life were:
- Brephos: a newborn
- Paidion: a child still nursing
- Paidarion: a child which can walk around and is beginning to grasp vocabulary
So again, how old were these children?
He didn't teach and bless them, He laid His hands on them and prayed for them "and then He departed".
Everyone is in need of baptism, even infants. We are born into sin, Psalm 50 says "I was brought forth in iniquity, And in sin my mother conceived me." Our fallen nature isn't about individual sins but about the curse of death every human inherits from Adam. We can not conclude what you think, because it would require us to invalidate many scriptures. And of course the kingdom of heaven is for "such as these". He already explained this previously, in Matthew 18. "Unless you are converted and become like children, you will not enter the kingdom of heaven." And what did He mean by "like children"? "Whoever then humbles himself as this child, he is the greatest in the kingdom of heaven." Children are humble, and have a simple joy and faith. He's not suggesting we become sinless like children. We don't "become sinless," our sins are forgiven. We become humble, we become pure and simple in our faith, by God's grace.
Your logic belies a fallacy that if a person is without sin, they don't need a savior. This is the error of Pelagius. Even a sinless man, were such a thing possible (it's not) would
still need a savior, because Christ was not simply a sinless man but the God-man, and He united deity with human flesh, redeeming all mankind from death in Himself.
A household included everyone. Jewish children were circumcised on the eighth day. Colossians 2:11-12 is one of numerous references that show that the baptism we undergo is a circumcision by God of our souls. Circumcision isn't limited to adults. Just as circumcision was the sign of the covenant between God and Israel, baptism seals us with the receipt of grace to enter into the new covenant, a spiritual circumcision "performed by Christ and not by human hands."
Your mere intellectual belief is the same error in logic I addressed above - that somehow by our meager "belief" or "understanding" we can be worthy of the divine blessing by Christ.
Infant baptism was practiced uniformly, by the entire church, as far back as we have records. The lone ancient dissenter was Tertullian, and he references sponsors. By this very witness we can see that the practice of baptism of infants with sponsors was already in effect (around 200 AD).