Being sensitive often makes people nervous. They have to pay more attention to what they say around you. And more aware of how they affect you- and by extension how they affect other people.

Being called too sensitive usually means that the person is not comfortable with how sensitive you are. So it might be more honest for them to say, "You are too sensitive for me."

I always wondered if sensitive is feeling things deeply, how can you be too sensitive? Perhaps you can take things too personally, but technically that is not too sensitive.   

Someone saying you are too sensitive shifts the issue onto you. It implies there is something wrong with the way you feel.

You might point out, "It seems that you are not comfortable with me being sensitive." At least it clarifies what the issue is. And whose issue it is.

So keep being sensitive. Don't let anyone talk you out of it. There is absolutely nothing wrong with feeling things. It is actually quite courageous. And very human.