I took the liberty of transcribing a portion of the Table Talk discussion of Dr. Iain Duguid when he visited our church back in 2016. Here is explains what baptizing covenant children means to the parent and what it says to the child:
What I am doing in baptism is I am saying to my child, “You are not free to decide for yourself what you believe.” You have already been claimed. You’ve already been signed and sealed. Now you can rebel against that. But you are rebelling against something that already marked you… There are all things in life, my child, you can choose for yourself… But when it comes to your belief. You’re not free. You’ve been claimed. You’ve been bought… Baptism is deeply connected with our understanding of salvation… Salvation is something fundamentally that God does, not something that we do, which means He is going to do something to our children. It’s not something that we have in our power. I can make my child a good little Pharisee… keep all the rules… I cannot give them a new heart. Only God can do that. And so where is my hope that God will do that? Well, God has given me promises in His Word. And so this is a sign and seal, not just for my child, but this is a sign and seal for me as a parent looking at this little child thinking “You are so messed up because you are my child” … [My] environment that I’m gonna create for you. What hope is there for you, poor child? The same hope that I have, which is that Jesus has promised to be a God to me and my children. And if they look to Him with trust and faith in Christ, then He will be their God. And that’s an encouragement to me. Because I know I’m gonna mess up as a parent. I know that I’m gonna do things that I should’nt do and fail to do as a parent… But God is able to work in spite of me and through me. And be at work not just in my life. But also in the life of my children. Just as He was at work in the life of Abraham and Abraham’s children.