It may not have been the words but the tone? I know that word is a trigger word for people and at the same time, I've been on the receiving end of someone treating me poorly over the phone. I worked in an industry where I handled people's money. Sometimes my clients would have an error (as will happen) and some of those clients would call and attack me personally.

I think calling her insensitive was a personal attack and may have triggered her defenses. She sounds like she's trying to work with you and you were in an emotional frame of mind. Could she have handled it differently? Perhaps. She is human however. She might have been offering a complimentary session to help transition or to check in with you.