When an adult puts a baby under the water for the first time, most swimming teachers advise to expect one of a few reactions; your baby might be completely fine or they could be startled, they could cry, they could jerk their arms and legs or they might cough up a bit of water. Parents are usually advised to smile and encourage their baby, or perhaps offer a toy to distract them from their feelings.
If I feel upset, I hope someone will want to listen. If I tell my husband that something has made me feel sad, I expect him to empathise, not smile at me and tell me it's okay, and then give me something pretty to take my mind off it. When babies cry after having been submerged, they're giving us a message, and they want us to pay attention. As parents, it doesn't build trust if we do something to our baby that they wouldn't choose to do themselves, and then try to smooth their feelings over - if we give ourselves the right to dunk them, they have a right to feel a bit cross about it!
To build a genuine, respectful and trusting relationship in the pool, I always advise parents against putting their babies under the water. It doesn't foster trust in the pool, and it definitely doesn't guarantee water confidence in the long term. If a child is doing something to communicate during the lesson, we pay attention and attend to it. We don't adapt the world, distract or cajole to prevent our babies ever feeling anything uncomfortable, but at the same time we need to be aware that we are physically manipulating a baby more in the pool than we generally would on land, and there comes a time when the baby might well have had enough of being held or moved around by an adult.
So if your baby tries to tell you "no" or indicates in some way that they've had enough, take a step back. Take baby steps and work at their pace, and don't think of swimming as doing things to your child - let them do as much as they can themselves.
If you belong to a swim school already who encourage adult led submersions, remember that you are paying for the instruction and can choose to follow as much as you agree with - your relationship with your child, and building their trust comes first.