equivocate

be deliberately ambiguous or unclear in order to mislead or withhold information

Latin aequivoocus, from aequus equal + vox voice

“Still, I am helpless, I cannot move, until I am assured that my daughter's reasons are such as a father need not underline." "Does the lady, perchance, equivocate?" "I have not seen her this morning; I rise late.”

— George Meredith, Complete Project Gutenberg Works of George Meredith

Imogen stood at the intersection of Sylvie and Esme, equivocating when her friend asked if she wanted dim sum or poutine. "Both sounds wonderful," she said with a smile, avoiding choosing either, much to the confusion of passerby in their vibrant Toronto attire.

At the corner of Götgatan and Hornsgatan, Hugo dodged questions from a nosy journalist about his secretive new invention. With a sly grin, he equivocated, weaving a web of vague promises and mysterious hints that left the reporter more confused than curious.