Geez >> When someone tells me I'm sensitive to me it means that my feelings are out of bounds for the situation.
Or it means that they don't want to "waste time" (in their estimation) considering how best to approach something, they just want to do or say without thinking. Which is at least immature, IMO
>>> That I don't have the right to my feelings of hurt or disappointment etc..
Right, and that they are negating your right in advance.

Some words are triggers; this one is for me, too,and I yelped when T said that I was sensitive. We talked a good bit about this; she said, wonderingly, "But it's good to be sensitive; I'm sensitive."
I looked at her and said, huh, yes you are, aren't you? realizing that she is also reasonable and authentic.
On her, sensitive looks good. Probably on you too!