mislead; attempt to conceal the truth
If you equivocate while giving testimony in court, you face the danger of being charged with perjury -- a very serious charge.
aequus (equal)#vocare (to call) (Latin)
equi (equal) vocal (sound). if we make similar sounds then it would be ambiguous (unclear) to distinguish!! equi+vocate sounds like advocate. corrupt advocates LIE, to CONCEAL THE TRUTH which MISLEADS the judge.