Your feelings, emotions, and expressions thereof make other people uncomfortable. That's it. Essentially these three phrases above (and many more) are designed to help the person you are being vulnerable to escape your emotions which they are not willing to deal with. It has nothing to do with you as a person. Nothing to do with your being weak, or emotionally unstable. No, it has to do with other people not wanting to confront their own emotions by having to deal with yours.
I am proud to be sensitive. Sensitivity is not synonymous with weakness, it's synonymous with great strength We love too much, give too much and hurt too much but somehow we are built to withstand any emotional storm and come out the better for it. So for those who can't deal with my sensitive nature, BE GONE! Because like the great Sammy Davis Jr. once sang "I gotta be me."