“For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call.” Acts 2:39
The word for children used here in Greek is “teknon”. According to the Greek Lexicon it literally means a male child. But can also be used for plural children regardless of sex. Some might say that that simply means offspring. In a sense that’s true, but if he meant generational offspring the word used would be “genos”. So in this sense the correct understanding is literally “children”.
It seems clear to me that Peter is commanding the children to be baptized into the promise.
It is true that in this passage Peter promises that the “gift of the Holy Spirit” is promised not only to the adults, but to “their children.” This verse is used by many to argue on this basis that baptism must be administered to children of believing parents.
In my opinion, this interpretation reads too much into the text. We must note that Peter goes on to say that the promise is “for all who are far away.” But no one interprets Peter to be suggesting that we should therefore baptize all Gentiles. The promise is for them in the sense that God wants to pour out his Spirit upon them (Ac 2:16). But they only become recipients of the promise — and we should only baptize them — when they make a personal decision to repent and believe in Jesus Christ. This is why Peter immediately adds that the promise is for “everyone whom the Lord our God calls to him.” It is not for everyone in general. It is for everyone who will repent and believe, and thus for everyone whom God calls.
The same holds true for Peter’s assertion that the promise is not only for the adults in Peter’s audience, but for their children. God wants their children to receive the Holy Spirit, but the promise is only applied to them, and we should only baptize them, when they personally repent and believe.
Defenders of infant baptism argue that the references to households being baptized in Acts suggests that infants were baptized along with adults (Ac 11:13-14; 16:15; 30-34; 18:8). There is no reason to assume this, however. When considering recorded history at this time it was the norm that all servants were included in a “household” in the ancient Roman world. Children, however, generally were not. This seems to be Luke’s perspective, for in the same context in which he speaks about households being baptized, he speaks about households being taught, believing and rejoicing (Ac 16:32; 34; 18:8).
Again, it’s important to notice that every example of someone “actually” being baptized in the New Testament was of a person old enough to decide to follow Christ on their own.
Never do we read about infants being baptized.
For example, it was only after the Samaritans “believed Philip” as he preached the good news that “they were baptized, both men and women” (Ac 8:12). It was only after the Ethiopian eunuch embraced the good news about Jesus that he was baptized (Ac 8:35-36). The apostle Paul was baptized after he encountered Jesus and obeyed the heavenly vision (Ac 9:18).
Even Peter, he commanded Cornelius and his household to be baptized only after he saw evidence of their faith in Jesus Christ (Ac 10:44-48). It was only after God opened Lydia’s heart and she believed that she and her household were baptized (Ac 16:14-15). And it was only after the disciples of John the Baptist accept Paul’s teaching about Jesus that they were baptized and received the Holy Spirit (Ac 19:5-6).
Without exception baptism follows faith and constitutes the first act of discipleship made by a responsible person who has decided to turn from their sinful way of life and submit their life to Jesus.