What this whole thing comes down to is really using the power of strange words to undermine norms which allowed bad behavior. The term mansplain appears to have been born in 2008 about a month after an op-ed titled Men who explain things, which begins with a personal accounting of a story in which she, an author of a recently published book, gets dragged into a conversation about the topic of her book and the man talking to her takes way too long to hear that his lecture on a book of the same topic is actually about her book. She also describes being reprimanded at a dinner for talking about Women Who Strike for Peace and their role in taking down the House Committee on Un-American Activities, the man explaining to her that the committee didn't exist at the time she said it did, and even if it did, the women activists certainly couldn't have had any role in its downfall. Turns out, she wrote a book on the events relying on historical documents and interviews with individuals involved. It describes a phenomenon that is pervasive in our culture where too often men assume the incompetence of women and condescend to them without regard to the woman's intelligence, experience or any other indicator of her competence with regard to the subject at hand.

When mansplain was coined, it called attention to the fact that so many women had frequently experienced the problem for their entire lives. It reflects that there is a common abuse which has a very consistent pattern of men undermining the credibility of women through condescension and correction. The reason that it caught on and has lasted at least this long is because women still experience the phenomenon, and many identify it as a constant struggle in their lives.

To the point of hypocrisy, I don't see the word itself being hypocritical; it is simply a term describing a common phenomenon. The closest I can come to sympathizing with the idea it is hypocritical is to acknowledge that it is sometimes over- or misused, and that often people who do misuse it are overzealous in defending their use of it. That sort of thing happens all the time during interactions where power is involved, but calling wolf on racism, sexism, ageism, and all of the other -isms isn't a sign that those things don't exist, it just means that sometimes individuals are wrong.

Lastly, to sexism, I think that the feeling that the term mansplaining exists implies that users of the term feel all men do this is an overreaction. Simply, the term was born to describe the too common experience women have of being condescended to by men simply because they are women.

As an aside, whitesplaining is a thing, and to lesser extents, the other -splaining that you talk about is too. The reason that whitesplaining or manslplaining has any meaning, though, is that it reflects the power that whites and men have over other groups in social interactions; we have strong cultural legacies of men, and particularly white men, having more property, more influence, and being afforded more rights than other people and it is clear throughout history that these advantages carried over into conversation and other social interactions. These -splaining terms just give a succinct way to call out behaviors which still undermine the authority, credibility, and standing of groups when race and gender are factors in the interactions.