Do you think some fans have this slight misconception that Katniss is the one more likely to shut Peeta out when we see in the books that when Peeta gets in his head, he sort of withdraws for a bit?
The biggest instances of emotional disconnect between them are caused by Peeta. After their first games he withdraws and doesn't speak to her or see her until the victory tour, and then when they're prepping for the quell he goes all Coach!Peeta and doesn't offer her any affection or friendship.
He has a really low sense of self worth and has a habit of withdrawing when he's triggered, probs thinking people are better off without him. He does not think he's needed or worth while and doesn't see that it hurts her when he pulls back like that. Its one of his biggest flaws and I think it makes a lot of sense with what we know about his personality and his upbringing. I love that every time he does this, Katniss is ready to accept him back with zero judgement. She literally falls right into his arms on the train back to the capital for the quell.
Katniss does pull away from Peeta a couple of times too. She's briefly pissed after the "you're so pure" incident and doesn't let him in her room (for ONE DAY) and then she avoids Hijacked!Peeta for a while in Mockingjay. This to me is not equal to Peeta's shut outs. Hijacked!Peeta physically and emotionally hurts her. She's shutting down because she's lost hope that he can be saved, because Peeta has always been hope for her and without him there to guide her she's very lost in the pessimism and darkness. It's a much more valid and fair avoidance I think. She's hiding from abuse, Peeta is not himself, and when Haymitch convinces her there is a chance she can help Peeta she does a 180 and gives him her best shot.
So yeah idk where fans get the idea that Katniss is the one who shuts Peeta out and not the other way around. Being an avoidant little dumb dumb is Peeta's bag not hers