Antonyms of insinuate:
announce, declare, proclaim, elucidate, explain, spell out, delineate, describe, eject, eliminate, exclude, expel, extract, withdraw, deduct, detach, subtract, reject.
Examples of usage:
  1. You will see, then, that my family pride and my worldly ambition are not founded altogether on those basements which move my laughter in another; if my feelings thereon are really, however, as you would insinuate, equal matter for derision, behold, my Julia, I can laugh equally at them!
    "Paul Clifford, Volume 6.", Edward Bulwer-Lytton.
  2. Well, he raved like a madman, declared that I had taken advantage of his absence to insinuate myself into the king's favor, and commanded me to obey him as the head of the house, in the name of my father.
    "The Complete Historical Romances of Georg Ebers", Georg Ebers.
  3. " You mean to insinuate-" " Nothing," continued Maitland, finishing his sentence for him, and then quietly ignoring the interruption.
    "The-Darrow-Enigma", Severy, Melvin Linwood.