He knows people make fun of him. He figures there's a reason. When he was a kid, it was because of his hand me down clothes, because he couldn't speak properly, because he couldn't hear, because "that Barton kid is just weird".
Little did most other kids know it was because his dad beat the shit out of him that he couldn't hear, that the hand me downs were because dad drank up all the money he earned. The weirdness couldn't be explained by one terrible parent, but rather by the diagnosis he gets a lot later in life, after the circus, after being taken in by the Avengers. It's during his marriage to Bobbi that he reluctantly visits a psychologist, who makes him take tests, and observes him.
He's uncomfortable, being watched this closely. It's his job to watch people closely, to have an oversight of the situation, something that is undeniably a useful trait for an archer.
At age thirty five, people make fun of him because he plays dumb, and because he fucks shit up, more so than is probably expected of a thirty five year old, and an Avenger at that. (Though, if Clint's entirely honest with himself, he's nowhere near the most dysfunctional of the lot. At least he doesn't have a substance abuse problem, and hell, even Cap had one of those.)
Clint Barton has enough insight into how his brain works to know he doesn't intend to screw up every single meaningful relationship in his life. It's other people he doesn't have the insight in. Not just women, though a lot of people seem to think his inability to have a normal relationship extends only to women.
It's with everybody.
For somebody who has a good view of his surroundings, and can flawlessly hit his target at truly magnificent distances, he has little to no view on how people work.
Barney helped him with it, when they were kids, and later the circus, where he was taught that if you can bullshit hard enough, people will believe you have people skills aplenty. It taught him the nonchalant body language he uses when he's not alone, taught him to read people better. (Eye contact was never an issue, you've got to look at people to read their lips, so it was a skill born out of necessity.)
But despite all the things Barney and the circus taught him, he'll never be great with people.
It's when Kate leaves that he realizes this, no matter how hard he tries, he keeps fucking up the whole interpersonal relations thing. And that no matter how hard he tries, it will never change.
The only one who seems to understand, in her own strange way, is Natasha. Perhaps it's still the cultural gap between the rest of them and her, or because she was raised by the Red Room, or maybe it's because Natasha is more like him than she seems at first glance.
The same, but different. Where Clint enjoys the company of others, Natasha seems to dislike getting too close to anyone, even if she can fake it better than Clint ever could. (Her training, no doubt, just like his own training had its own perks.)
And maybe that is why it worked for some time, between the two of them, and why it ended, in the end. The combination of two people, with their own oddities. But in the end, too many oddities to work well together. Perhaps if he had been more like her, or she had been more like him. (Or perhaps if Natasha hadn't been raised in the Red Room, or if he'd been Russian as well.)
But despite all that, even when he doesn't count all the reasons why he admires the Black Widow, he admires her because of the way she fits in, despite all the possible reasons she doesn't.
Admiration, and some jealousy, because people don't seem to react to her seemingly strange behaviorism the way they react to his.
But everything is not terrible. Things have their definite perks too.
Like the reason he's even an Avenger in the first place, his archery skill, and general weaponry knowledge.
Sure enough, he was trained by the most skilled men there were, but if he had been normal. (He has to correct himself every time he thinks that, he's no less normal than anyone else, his brain is just wired differently.) If he had not been the way he is, there was no way a kid like him would have practiced relentlessly. He would've been distracted by the million and one things there are to do when you're travelling with the circus.
Because even if you live the circus life, it's still a whole different world from the one you lived in when your parents were still alive.
It also helped that there were no distractions when he shot. A singular gift of focus, and no distraction from sounds around him. Missing is nigh on impossible when you're able to focus like that, and have trained so long, and so hard.
And he's not always sure if that doesn't just weigh up against people thinking he's weird.