I taught swimming lessons for a while, and I still remember this one little boy. He was about 5 years old, and he didn't mind wading out to his neck, but he could NOT put his face in the water.
We could get him to touch his nose to the water, and them he'd freeze up- and shake like a leaf in a high wind. He didn't even mind being splashed in his face as long as it wasn't hard, but he could not get his face underwater.
He finally did learn to paddle around a bit, but he always had to have his face high. this was close to 40 years ago. I still wonder if he ever overcame his phobia.