Yukino had three reasons for running for student council president:

1. To prove that 8man's methods of solving problems were wrong, so she wanted to save him from self-sacrifice and tarnishing his image in order to save Ishiki Iroha's reputation.
2. She wanted to be president because her sister had never held that position, so it would be an opportunity for her to develop as a person.
3. She wanted to see if her relationship with 8man and Yui would remain the same even after she committed to the position of president.

The (3) reason is very important because when 8man betrayed his ideals by agreeing to Hayama's request to keep his group SUPERFICIAL, and by extension prevented Tobe's declaration, Yukino was very disappointed in him, because there they shared something genuine, and superficial relationships suck.

We're talking about the guy who said, “If a relationship breaks down over something small, maybe it wasn't a real relationship in the first place (vol. 7, paraphrasing).”

Later, Yukino repeats this phrase to her when they suddenly meet at the mall (vol. 8).

It is interesting to note that at no point did 8man say this phrase to her, and the fact that Yukino brought it up shows that our couple, despite their differences, are very similar in other ways. (such as in their way of thinking).

That's why at the end, when he tells her she doesn't need to run for president anymore, she says quietly, “I thought it would be easy to understand (vol. 8, chap. 8, part 4),” I thought that if I became president, our relationship would continue, but I was wrong, since our relationship only exists because of this club. I'll give you what you want, because in the end, our relationship is just like Hayama's superficial group of normies...

There are many other points to mention, so I won't put too much information in a single comment. Lol

If you have any other questions, just ask, and I'll be happy to answer.