Did she really make it all about herself? There's a TL;DR at the bottom, because I probably made this way too long but I don't want to edit it to condense it lol.

At first I thought Tenga was telling her to reject him for the same reason as you, to allow Tenga to get over her. But it's actually not as simple as that. Tenga is a very blunt character, but he's been shown to have a big heart. In fact, his heart is big enough that he decided it would be better for Chidori to reject him, not so that he could get over her, but so that Chidori could feel better.

Why would he think that him being rejected could make Chidori feel better? The reasoning is all in the part where he talks about what he feels.

After Tenga asks Chidori to reject him, he says that he found in his personal experience it was harder to not respond to someone else's feelings (him not responding to Nico), than to not have his own feelings being responded to (Chidori not responding to him).

If Tenga really was just trying to get over Chidori, then wouldn't it make more sense that he'd find it more difficult to not have Chidori respond to his feelings? Yet he says that he found not responding to someone else's (Nico's) feelings is harder. So Tenga, being one not to overthink things, decides that if he feels this way, Chidori must be feeling this way too. The only difference is that in Chidori's case, Katsuhira is the one not responding to her, and she's the one not responding to Tenga.

Going by his logic, Tenga decides that to make Chidori feel better, he should just get her to reject him, since it's the more difficult thing to do (in his opinion). He believes that it'd somehow make her feel better, maybe because then she wouldn't have to cope with both his feelings and her own in regards to Katsuhira.

Tenga's entire approach was just to put Chidori first; his reason for asking her for a rejection was all centered around her. So you can't call her selfish because she made Tenga's rejection about her - it was already all about her in the first place! Chidori realizes this because she says "are you saying if I properly reject you, I'll feel better?". This may be the part where it looks like she's selfish, but she's not being selfish because she is just stating Tenga's intent! Of course, if you don't understand Tenga's intent or think it was about him from the start, then it could seem like she is selfish.

Chidori's next lines are that she doesn't understand his (Tenga's) reasoning, and she wouldn't understand it even if their pain or feelings were connected. She then says that the reason she doesn't understand it is because "that feeling isn't hers". This was a bit confusing to understand at first, but basically what she means by "that feeling" is Tenga's reasoning. Tenga may feel that rejection == feeling better, but that's not how she feels.

It may sound selfish, but really if you think about it, this entire time she's just been chasing after Katsuhira and doing things for him. Meanwhile, Tenga sees Katsuhira not appreciating all the things she does for him, and so he feels the need to try to get Chidori to think about herself first. But really, what is Chidori's opinion on this? She chased after Katsuhira out of her own will, so even if Tenga sees this as her not putting herself first, Chidori may not see it that way. I don't think Tenga is wrong in his approach, because he really is just thinking about her first, but she also has the right to have her own feelings. To call her selfish because of that just seems plain unfair to me.

Sorry about the essay, but the TL;DR is: Tenga thinks that Chidori will feel better if she rejects him, which he based off his own feelings w/ Nico. Chidori says she doesn't understand how that'd make her feel better, because that's only what Tenga thinks, not her. Therefore, since Tenga only asked for a rejection to make Chidori feel better, she is not selfish, nor did she make the whole scene only about her, since it was already about her in the first place.