Some parents believe, on reflection, that a service of baptism is not the most appropriate service for them and their child. They may think it is too weighty in terms of their own faith, or that the promises involved go beyond what they can say with integrity.
Some parents may be adopting a child who has already been baptized.
Some may have a child who was baptized in emergency circumstances in hospital or at home.
Other parents, who may themselves be committed Christians, feel strongly (because baptism is so meaningful) that they want their child to be able to ask for baptism, if and when they are ready to respond for themselves.
All nevertheless want to thank God publicly now for the safe arrival of their child and express their love for that child. This can be done at a service called an 'Act of Thanksgiving after the Birth or Adoption of a Child'.
If you are not sure whether Baptism or an Act of Thanksgiving would be more appropriate for you and your child, talk it through with your minister, who will be able to advise.