evasiveness
The habit of avoiding clear answers or the truth.
Evasiveness is the quality of avoiding something, especially questions, topics, or responsibilities that someone doesn't want to deal with directly. When a politician practices evasiveness during a debate, she might answer a tough question about her voting record by talking about something completely different instead. When your friend asks if you broke his favorite pencil and you respond by suddenly changing the subject to lunch plans, that's evasiveness.
Someone showing evasiveness dodges or dances around the truth rather than giving a clear answer. A student caught copying homework might use evasiveness by giving vague, unclear answers when the teacher asks about it, hoping to avoid admitting what really happened.
Evasiveness feels slippery and frustrating to people on the receiving end. If you ask your sister a straightforward yes-or-no question and she responds with evasiveness, giving you a long, complicated non-answer, you'll probably feel annoyed. The evasiveness itself often reveals that something's wrong, because people usually only avoid questions when they're uncomfortable with the honest answer.