You can learn.
I honestly believed that my daughter would never learn. She just wasn't getting it, class after class after class. After a few years of trying in group lessons, I pulled her out and put her into private 1:1 tuition. By that time, she had developed a serious phobia of the water and every single lesson was traumatic. She would cry before the lesson, cry during the lesson and cry after it. I pushed her to keep going.
I can't swim myself and was desperate for dd to master this skill while she was still a child. I believe it's a really important life skill, and I have missed out on so much because I can't do it, so I felt that I'd be letting dd down if I allowed her to quit. However, when the private lessons didn't seem to be working, after all the trauma, I was ready to give up and abandon the whole project. It just wasn't worth the stress.
To my great surprise, when I told dd that she could give up, she said that she wanted to keep going. She reasoned that all of the stress and tears would have been wasted if she didn't actually learn, so she wanted to push on through. She is a very determined kid!
Anyway, we persevered, and gradually, her fear of the water got less. And then, almost overnight, she cracked it! From that moment, it got so much easier, and she learnt how to do front crawl, back crawl, breaststroke, even butterfly. I could never have imagined that she would be able to do those things, but I am so glad that she didn't give up. She doesn't swim regularly any more, but enjoys it on holiday and can happily go and mess about in the pool with her friends at weekends. She isn't ever going to be an Olympic swimmer, but she is confident and could swim a fair distance if she needed to.
In fact, she has inspired me to try again myself. I'm planning to go on one of those intensive swimming course weeks where they promise to teach even the most fearful non-swimmers. If dd can do it, I figure I can too.
And so can you.