I'm not sure if you realize this, but your whole post was (ugh, much as I hate the term) a "mansplain." You are saying that as a male you know that a female's concerns are invalid because you know better than she does. Then, you cited an obscure example that really isn't relevant - sure in the case of a more experienced male employee mentoring a less experienced female coworker it's appropriate for that person to be explaining and teaching a female so long as she wants to be mentored. That's one very narrow case and doesn't represent the vast majority of male/female interactions. You are also saying that you know better about how females feel (or should feel) about their reactions with males better than they do.
The whole point is that while I think the term is annoying and can be misapplied, the situation is real. In normal discussions it's accurate 99% of the time it's claimed. They provided several good examples in the podcast of what it is and why it's infuriating to women. The right thing to do is acknowledge real problems, acknowledge and use real solutions to those problems, and ignore the politics.
The only time that "mansplaining" is misused at a high rate is when talking about gender relations politics. In that context, yes it is used as a way to shut down debate and discussion. That's not what was going on in this podcast, and it doesn't represent the real problem.