To dream of doing the backstroke represents a comfortable attitude to navigating an uncertain or negative situation. Not really feeling that a problem you are facing is actually a problem. It may also reflect a sense that an uncertain situation is too easy to get through. Enjoying taking your time getting through a difficulty.
Negatively, the backstroke may be a sign that you are too comfortable with a problem or uncertain situation. Taking your time or being lazy when serious action is required. Thinking that nothing matter when it actually does.