It also doesn't help when the escort mission does not suit the genre your game is. The Emma escort missions for MGS2 that was mentioned above is an example of this, though I think the worst parts of it (i.e. the timed underwater swimming) were more due to MGS2's rather crippling overreliance on gameplay gimmicks. I personally think that the EVA escort segment at the end of MGS3 was also pretty bad. You have to sneak through three stages where all of the guards are in permanent caution status (meaning they're aware you are there and are always actively searching for you, instead of just passively patrolling the area), and some are even camouflaged and are waiting in ambush.
Now this level would be a fairly difficult one if you're just on your own, but you also have to deal with escorting the female lead of the game through the area. She's been wounded, so moves at a snail's pace, needs to be constantly fed to ensure her stamina stays up and her rumbling stomach and whining about hunger doesn't alert nearby guards, and has a bit of a delay in her movements, meaning if you begin crawling, she'll take a half second to start doing it herself, which is enough time for a guard to notice her and raise the alarm.
You have a rudimentary command system of wait/follow, but if you wander too far away for too long, she'll eventually come out of her hiding spot to try and find you. You can tranq her and try to clear the area out on your own, but she talks in her sleep, which alerts nearby guards. You can knock her out by punching her in the face or throwing her to the ground, which stops her from talking in her sleep, but that lasts for a few minutes at most, and all of your codec team give you shit for it.
So the end result is that we've got a stealth game, where the player has spent the majority of time sneaking on their own and have probably gotten used to that idea, and at the absolute last minute (this segment is the last actual sneaking part of the game, after this is the final boss and around 20 minutes worth of cutscenes) they throw a lead weight around your neck and force you to do it with an escort that is constantly making noises. You're not fucking up because you're bad at the game, you're fucking up because the game is screwing you over.