I have never heard of the word "handicapped" being offensive... at least not to the point where it would warrant this type of response. I mean, how many times have you heard the term "disabled parking?" I'm guessing not that many, if at all.
I actually looked up the origin of the word, and Snopes gives a very detailed response.
http://www.snopes.com/language/offense/handicap.asp
Kind of interesting, actually.