That is speculation . the scripture does not say that. The reason which the scripture gives is this...
By the way , this is what follows afterwards , not " come and follow me "
Besides , it makes no logical sense to say Jesus was our example and then pick and choose what to apply it to. There are things which we do not follow his example in. Such as being crucified for other people's sins. Even the immediate context has Jesus immediately following his baptism with forty days of fasting. Are we expected to fast for forty days in the wilderness after our baptism ? On what basis is it decided which things are as an example and which things are not an example for us ?
Clearly , saying it was as an example for us is grasping at straws because the scripture does not say that directly. What it does say as a reason is difficult to understand and a bit of a mystery.
If the goal is to stick to only the scriptures , we are not faring well with the question concerning the baptism of Jesus. The point that i am trying to make is that just because the scripture is silent on a given point or just because it only gives hints at something does not make it any less true or false. We routinely piece together doctrines in areas where the scripture does not make a direct statement. there is room for honest disagreement between Christians who both want to serve the Lord and be true to the scriptures , yet reach different conclusions on some of the details. The more rigid and dogmatic that we are about all the details , the more likely that we have resorted to some speculation and educated guesses. We could go through example after example of this.
This does not mean that anything goes. But it does mean that there is room for different honest convictions. We are speaking of Christian baptism being applied to infants , not some pagan and evil ceremony. You are not forced to agree , but there is no scripture which directly forbids infant baptism.