If you sidestep a problem, you avoid discussing it or dealing with it. Rarely, if ever, does he sidestep a question He was trying to sidestep responsibility. = avoid
If you sidestep, you step sideways in order to avoid something or someone that is coming towards you or going to hit you. As I sidestepped, the bottle hit me on the left hip He made a grab for her but she sidestepped him
avoid or try to avoid fulfilling, answering, or performing (duties, questions, or issues); "He dodged the issue"; "she skirted the problem"; "They tend to evade their responsibilities"; "he evaded the questions skillfully"