The lighter side of ADHD
Everyone needs to go through that shit at least once... if you're lucky you can lean on your network of former co-workers to provide references that let you just be open "I suck at interviewing" from that point onward. I hope you eventually achieve this blissful state because I too cannot maintain eye contact for more than half a second.
"None of this has anything to do with your ability to perform the desired task" is the major flaw in this. Social interaction is a pretty huge part of any job where you work with people, and so-called "chemistry matches" are often rated as the top thing teams are looking for. This is why so many hiring managers will bring in other team members into interviews.
Edit: just because you don't like this fact doesn't make it less true. People want to work with other people that they don't want to strangle.