As in, a hurdle you wanted to cross, but didn't because of the difficulty, and ended up quitting the entire game because of it?

I'm not sure I remember doing that. But I did quit God of War after fighting one of the last optional bosses a couple of time.
However, I had already beaten the main game, and I had little interest in spending time on this boss when I could be playing a new game instead, so I guess that's not quite the same. But it's the closest example I can think of at the moment.

Nope. But that are sessions that I've skipped because they were too hard, or tried again in easier difficulty

But I've quit games because I've found them badly designed or annoying

I absolutely suck at games like Rayman Legends. I wanted to beat the game, or at least many of the levels. But I only got 1/4 way through before I gave up.

Only Sekiro because the game is super cheap and unbalanced. I also hated having to clear out enemies in order to be able to even challenge the boss. Other than Sekiro I have beaten every game I've bought.

7th Saga

No, I never back down from difficulty if the game is good, the only reason I've quit a game is for being boring or dissapointing as hell - Like Castlevania Lords of Shadows 2 for example.

Not that I remember. Most games have difficulty options that I could change anyway if I was getting frustrated.

Super Meat Boy. 3/4 through the game that one boss was way to hard and tedious, so I just quit.

Yep. Nioh, hardly got anywhere, don't think I even reached the first boss before I just got frustrated with it, just wasn't worth it (was free on PS+ anyway).

My buddy ragged quit on me last night! We were playing Back 4 Blood.

I played with some random and rage quit soon after but you have to pick yourself and keep coming back for more punishment.