When you are unwilling to make a decision and almost intentionally go back and forth between two choices, you are equivocating. When politicians equivocate, they are often afraid of upsetting, and thus alienating, voters with their decisions.
A key part of equivocate is the root vocate, which comes from the Latin vocare or "voice." When you give your voice to two opposing views in order to mislead or keep your options open, you're equivocating. Think of the expression, to talk out of both sides of your mouth. If you want to go to a party and your parents keep saying "maybe, it depends," tell them to stop equivocating and give you a straight answer.