The thing I want to know is what does Yozora wants I just do get her sometimes.
Yozora just wants to be alone with him and no other should be around and disturb them.
In their childhood they were both outcasts and had no friends so they share the same fate and they only had each other. Yozora has some romantic and nostalgic memories about that because it was the only time in her life she had a very good friend. And of course - Yozora is a girl and Kodakas declaration to care for her more than 100 friends can be also understood as a confession of love if it is directed to a girl. So Kodaka was her first love/romance after all. She was to shy to reveal to him that she is a girl.
The moments with Kodaka were the only good impression of friendship she ever achieved, so she clings to them.
After seeing that the present Kodaka is still an outcast she had hopes that they can recover their old friendship to the old state. And of course mainly alone together like 10 years ago. She fooled him into joining the club so they have a quiet place for themselves. The recruiting poster Yozora made was encrypted so her original plan was that no one else should join the club. After Sena joined, Yozora had to move on with her deception and now the real club activities started.
Yozora is confused why her plans don't work out because she still thinks that nothing has changed between them and they are just alike (both are outcasts and always alone and have no friends). But of course that is not true.
Kodaka don't want to be an outcast any more and he really want friends - and of course not only one. He enjoys to be in a group.
Yozora don't mind staying an outcast (she is used to be alone) as long she has Kodaka at her side. She has trouble coping with a group. She don't want other friends.
The old state was: Both were outcasts and had no friends. So Yozora also want that Kodaka himself should not have another friend besides her.
So she tries to shoo away the other girls (especially Sena). She tolerates Kobato because she is no threat for her.
Yozora has to come over her past because Kodaka won't accept her way of living out a friendship/relationship.