When I feel/get offended by something someone has said, I usually try to provide context as to WHY I'm offended by it. This not only gives them the opportunity to let them examine the issue from a different angle, but it additionally gives them the benefit-of-the-doubt by allowing them an opportunity to clarify, "Well, THAT'S not what I meant by it -- HERE'S what I was trying to say."

Likewise, if my words offend someone, I appreciate them telling me why. Otherwise, it DOES indeed seem like an attempt at gaslighting or a character assassination against me, if they're unwilling to illustrate for me the impact that my words had on them.