I would put it this way, it emphasizes the fact that in the end something didn't happen regardless of an attempt/effort to make it happen.

- Why do you like to remind me that ended up not getting married?! (it should be мне not меня) - She tried to recall where she might have met him, but eventually she couldn’t - I wound up not understanding that/ at the end of the day I didn't get it так и не means something along the lines of, that something started but never resulted in anything, hope you got what I want to say here

You might say that "так и не" means 'after all that was before you have the result". And that result is negative. Probably this is not the best explanation) so here is an example: "Она пыталась решить проблему, но так и не решила" - "She tried to solve the issue but didn't manage to"

Grazie mille Евгений :)

Just a short notice that might be some of help to you if you don’t mind. «Так и не» is commonly used when the event is highly expected to happen: Он изучал русский самостоятельно, но так и не выучил (he learnt Russian by his self, but he didn’t learn it). So in this example we highly expected him to learn Russian but he didn’t do that, this is why we use «Так и не» here. In addition, «Tак и не» normally requires the perfective form of verb after it, like ‘выучил’ in the example above. It also tell us that one purposefully tried to do something, he wanted to do that, but he didn’t manage to do it. So we use "Так и не". Let me know if you need some more examples. Thanks for the question! Arrivederci!