If the crying is not a result of anything you or the parent is doing (intentional or accidental submersions, forced back floating, etc.), and you can rule out that the baby is not feeling well (tired, hungry, teething, etc.), I'd look at two common possibilities that could affect the baby's level of comfort a the swim lesson. At 6 months old the water is a natural place for a newborn, so just "being in the water" usually does not cause the baby to cry or become upset. So what are some of the possibilities?
Air and Water Temperature
Problem: One factor is the water temperature. Babies need to be warm. I really don't want the water any cooler than 87 degrees, and I'd prefer it between 90-94 degrees. The second factor is the air temperature. If the baby is being held with the majority of his/her body out of the water and the air is cool, then the air temperature could be making the infant uncomfortable.Solution: Hold the baby a little lower in the water (keeping the mouth and nose out of the water at all times) or try a baby wetsuit.
Position
Problem: The second cause for infants or babies to cry in swimming lessons is often overlooked. I was reminded of this technique again just yesterday evening as I held my 3-month old baby boy at home. He was not happy about something. I didn't know what, of course, because he can't verbally tell me yet. What I did, and what most every parent does without even thinking about it, was I simply repositioned him. Instead of holding him in a cradle-like position, I moved him to a hug hold. Then that didn't work, and I moved him again so that his back was to me and he was facing the room, the TV, the action. Presto, no more crying!Solution: When parents and swim instructors have a baby crying in the pool, they often are rush to judgment that the baby doesn't like the water. They forget all the techniques in which they instinctively and successfully use at home. So solution number two, try different holds until you find one in which the baby is comfortable. What you do at home, often works at the pool too!
I find it almost funny, when I watch some parents with their babies in the pool. I'm exaggerating a little, but I feel like I have seen them hold their baby by the arm, the leg, the ear, etc. Find a comfortable position for the baby, relax, and enjoy your lesson.

