My problem with this softening caveat is that the speaker acknowledges that he will present his argument in a way that will offend/sound rude/make him look like a jerk. Instead of priming my listener for thinking I'm rude/a jerk/etc. through admitting that I am, I'll just think of another way to gently criticize. Playing to one's emotions is all about being convincing, and "I don't mean to be..." is an unconvincing phrase.

It's a way to convey tone through text. Sometimes the same comment can be taken in either a rude or a helping way, and prefacing it with "I don't mean to be rude" is a way of saying "please take this in the helping way."

When talking in person you can infer this through how they say it, but in anonymous text on the internet the disclaimer is helpful.

I've often found that one is better served by saying "please take this in the helping way" outright as opposed to relying on over-cliche phrases like "I don't mean to be X."

Being earnest and dare I say somewhat unique in your discussions can often produce better results than crutching on over-used phrases. This is a reason I stick to phrases like "I apologize for" over "I'm sorry for", or "I appreciate that" over "Thank you for." When words/phrases you intend to convey become noise or just another figure of speech, why bother saying them at all?