Both of my kids have freaked out over various things, sometimes for years at a time. The best I can say is that eventually they get over it -- they see other kids doing things long enough, or they forget about it over a long winter, or something.
My DS11 had that swimming problem for years, but just last year he learned to swim in the river. When he was two, three, up to about seven or so, he freaked out every time he even got a drop of water on him. He could be brushing his teeth and have a drop of water fall on his shirt, and he'd have to change his clothes. He didn't want to get in the water to swim, he didn't want to do anything but hang on the edge when he finally got in. Eventually he decided swimming with his friends was more important. He spent one summer mostly in the house because he had developed a morbid fear of bees. By the next spring, he had forgotten it.
DD7 has been a freak-out kid all her life. She went through a couple of years of being terrified of wind. She used to scream bloody murder if she saw even a speck of anything in her bath -- a hair would send her through the roof, but even a speck of dust or towel fuzz was grounds for a total panic attack. She had a horrific fear of dogs, even though we had one that she wasn't afraid of. These days, most of that has been blunted to a manageable level -- she can get hair out of the tub herself, and while she still asks if the trees are going to fall on us when the wind blows, she will actually go outside and play in it, and she's ok with dogs for the most part.
I think if you just keep explaining, keep calm, and let them figure it out from practice, it gets better. So far, anyway.
