One time in college, I told a classmate that I thought the school should provide us with milkshakes during finals, because some of us were unable to swallow solid food. My classmate said, "Well, suggest it," and sort of shrugged it off. But I didn't want a milkshake. What I wanted was to talk to someone about how sick to my stomach I felt all the time. I wanted someone to ask why I had trouble eating solid food.
I realize now that I have probably given similar responses, without meaning to blow the other person off. In high school, a friend of mine didn't like that her hair was curly, and I said, "Why don't you straighten it?" I was trying to help solve her problem, but looking back now and realizing that she never did straighten her hair makes me think that she didn't want styling advice any more than I wanted a milkshake - she wanted reassurance that her hair was beautiful just the way it was.
I am not always the best at reading people, but my new goal is to be able to figure out what people really want, and give it to them.