The role of the father according to scripture is to lead their families spiritually. There are many ways for dads to lead their families as they walk with Jesus. I know as a father, it is a privilege to lead my family though I am not perfect at it as much as the next Christian dad.
In 2009, my son admitted that God saved him from his sins and wants to get baptized. After talking with him to make sure he wanted to be baptized to he follows Christ, I baptized him two weeks after Easter Sunday. About two years later, my daughter acknowledged Jesus as Savior and Lord. Once again I was given the opportunity to baptize one of my kids.
Some of you are praising God for the fact that my kids are saved and baptized. Some of you maybe questioning why was I allowed to do that while other are wondering can a dad baptize their child. I know for many of my Paedo Baptist friends, the answer is no. A pastor must baptize their child. For some of my Credo Baptist friends, the answer will be depends on the church.
I will like to share my opinion regarding dads baptizing their kids. If you read the New Testament, you will see scripture does not command for clergy only to baptize believers. We do see the disciples, John the Baptist, and Philip baptizing new converts, but there is no command that churches leaders are the only ones to baptize.
As I mentioned earlier, fathers are given a responsibility to "bring (their children) up in the discipline and instruction of the Lord" (Ephesians 6:4). You could say the dad is a pastor in their homes. They are the ones who teach their kids spiritual truth. Yes, moms do assist them, but dads are the ones to instruct children. So if a child comes to Christ whether in the home, during a church service, or at a church camp, I believe the father should be allowed to baptize their kids. Now, if the dad does not feel he should and let the pastor do it, that's fine. That does not mean the dad is removing himself as the leader of the home.
I mentioned that it depends on the church for dads to baptize their kids. If you are a pastor or church leader and tell a dad he cannot baptize his child, you are taking away the blessing that man has in joining with his child the joy he/she feels in honoring Christ through baptism. When I got baptized, I wanted my brother to do it. The church would not let him because he was not ordained at that time. My youth pastor did baptize me, but if I asked my dad to do it, he would have been told no he cannot.
In my walk with Christ and as minister of the gospel, I have only be given the opportunity to baptize two people. They are my kids. If they are the only ones I baptize on this side of heaven, I will be okay with that.