After re-reading it, I think I get it.
The flashbacks show someone who was never really considered, and from that became emotionally adrift. He was Mr. Average. He got a game over, his sister said "hey come shopping with me," and the weight there is the flip on "Continue?" from 'yes,' what he wanted to do, try again, to 'no.' His dog passed away, and while his sister cried then, when he was alone, at night, he couldn't stop crying while looking at pictures of him and his dog hugging. He overhears his parents say that the dog was really attached to his sister. He's looking at the Hobbies and Special Skills section, and coming up with nothing. He has to look up what to say. We see him get slapped in public, but we don't know why. We see the smoking woman again, and she's telling him he's annoying.
We hear his thoughts here. Boring. Boring. Boring. At first, it sounds like apathy. But then, we see "I knew it. I really am a boring person." It wasn't apathy, it was self-criticism. He has internalized the idea that he's a nothing person.
He's about to return her hug, when her mom calls. He's happy about this, and he carries her inside and gets her all tucked in with stuff around that she needs, and I think the KEY here is that the second flashback starts as she hands him the letter. The flashback is about how he's lost touch with his friends, and how he didn't mean to, it just happened. He was working hard, but when he poked his head up he realized that... everyone else had things they were working for, while he didn't. The conversation then becomes about how the guy he's talking to really changed once he became a dad. He started feeling like there was something he really cared about. "If you ever become a father, you'll understand too. I'm sure of it."
So what's in the letter? Heartfelt thanks, and a heartfelt plea. She was anxious when her old manager went on leave, but he's been so nice and eased the anxiety. The letter says that she knows this is just his job, but she's happy. But that now and again, could he please spend some time with her outside of work, too? This makes him feel deeply guilty, because he's already decided he's not a good person who cares about her. He was just thinking of her schedule. He wanted to leave the decision up to other people. She's lonely and he's the only one around.
He's boring, remember? There's nothing to him.
I think people are missing the most important part about when he starts flipping out inside. It's not when she touches him. It's after she says "I wonder if this is what it'd be like to have a dad." That's when he starts screaming inside for her to stop. He's begging her to stop. It's not about touch, it's about connection. It's about that she genuinely trusts him and wants him around. He can't handle that. He's not going "OH LAWD DO NOT MAKE ME TOUCH YOU I WILL HAVE THE IMPURE THOUGHTS," he's begging her to not get close. To not care about him. To not make him important to her. I think there's lots of potential reasons why, but the easiest one for me to understand is that... well, nobody seems to have ever done that before. Becoming a figure in this girl's life, being someone who matters to someone, is new to him. He doesn't know how to handle it, and he has already internalized that he doesn't deserve it.
Cause when he walks out, and he both physically and metaphorically looks back, the only person there is Ayano. Telling him that she wouldn't know what to do without him. Telling him she's glad he's there.
I don't see that last panel of him in the car as anguish. I see it as him being overcome with emotions he doesn't know how to process. Because, for the first time he can think of, he matters to someone else.
