In this sub I often see this story: "My wife cheated on me with a coworker, then she accused me of cheating on her, even when I've never even thought about cheating. She made the accusation without any hint of evidence, even though I only confronted her after gathering iron-clad evidence, how can she do this"?

If you see things from her perspective, this is actually not hard to understand at all. So you already said you both agree that she cheated, because you confronted her with hard evidence. This means she knows it's "out" that she's a cheater. Let's say you're not a cheater. Well, then she's the "bad" person, and you're the "good" person right? You might think, objectively, probably yes. But that simply cannot be. She simply cannot emotionally handle the fact that she's the "bad" person and you're the "good" person. She simply cannot emotionally handle it!!! So she simply makes herself believe that you cheated, because then in her mind, she's no longer the only "bad" person, you're just as "bad". Since she already believe "you're a cheater" in her heart, she can easily throw out accusations to her friends/family/everyone around her, she can make up all kinds of details since she already believes it happened, and that's all that matters. To drive the point home, why stop at believing you're a cheater, why not believe you're a worse cheater than her? If she cheated once, she only need to believe that you cheated 3 times to make you the "bad" guy and her the "good" guy. See, it's just that easy. You actually cheated 3 times. Once this year, once 2 years ago, once 5 years ago, see how easy that was? What, you're saying she has no evidence? She requires no evidence to believe herself.

A simple extension of the above argument can apply to accusations of child abuse. I'll leave to you to fill out the blanks.

I understand that I'm playing "devil's advocate" and in a way excusing what women do. Maybe I'm almost victim-blaming here. All I'm saying is, this is my guess as to motivations of women. In some situations, maybe it's better to just accept how cold they are, and take things from there.