Some people do get offended at things that you and I would not even notice.
Without knowing the full story, it may not be that the nurses are offended by being called "honey" but rather "cupcake" or any number of other terms that he hasn't mentioned. Or perhaps the WAY it is said by the OP is what bothers those who have complained...I suspect, given his previous posts, that the terms are not used as a friendly expression of affection with those with whom he is friendly, but rather as a derogatory term and are said in a snide fashion. Or perhaps these comments are accompanied by unwanted sexist remarks or physical interactions. If you have read his previous posts, you'll see he decided to start calling the nurses "sweetheart" so as to emulate one of the more hated CT surgeons on staff there who does that. Referring to women by such terms normally reserved for affectionate relationships when you are meaning to derogate them is insulting and belittling. It is a "there there little woman, don't worry your pretty little head about it" type of comment and many women ARE offended by its usage in this fashion. Most women are not offended by the use of the terms when they are used in a friendly fashion such as expressing appreciation for a job done, "thank you for helping sweetie. I really appreciate it." However, you have to be careful as some are offended by any such usage in the work place.
I don't know the OP; none of us do. However, many of us responding here have seen enough of his posts (which admittedly may be pure fabrication and/or not reflect his IRL persona) and enough of these situations to take them seriously.
Is it fair that men get hit with these complaints as frequently as they are? NO...as you note, some people are looking to be offended. But this thread, and my responses, aren't about what is fair. Its about what should be seen as a serious matter and addressed as such. This isn't about justifying whether or not the treatment of the OP is "fair"...his employer is REQUIRED to address these issues if they are raised. For all I know he's totally innocent of the charges...for all I know, the program has a problem with him and this is a way to get rid of him.
I personally don't care if someone calls me honey...although my attendings tended to prefer "Kimmy", "kiddo", "KC" or "sweetie" (the latter more of a reflection of my frequent use of the term with colleagues)...but there are plenty of others that do and I suspect there is more behind the OP's story than he chooses to tell.