Meaning here
01
insinuation
noun · /ɪnˌsɪnjuˈeɪʃən/
An unpleasant accusation or suggestion made indirectly.
Still unclear?
He means: you accused me without saying the accusation openly.
What the wording does
He tries to move the argument away from whether the accusation is true and towards whether it was polite. The narrator refuses that escape.