be honest

I thought we had good conversations and I didn't talk about anything we weren't supposed to (boys, booze, Barack etc) so I don't understand why they didn't invite me back

That question is really hard to answer without knowing anything about you, there can be any number of reasons someone doesn't get asked back somewhere. It could have just not been not a good fit, or it could have been bad luck, or something in between, but there's really no use overanalyzing it, it is what it is. If you genuinely like kappa and want to go out for spring then by all means do, but also make sure you're considering these sororities for the right reasons because from reading this post it doesn't seem like you are and most girls can probably pick up on that during recruitment

It's possible that the conversations you had just didn't click with the sisters that you talked to and you might have better luck with other members of the chapter. That said, it's more likely that you just weren't a fit for those three chapters. Kappa isn't the only sorority doing Spring recruitment, so if you're really interested in joining a sorority you might want to check out Chi O or one of the other chapters that are having it. If you feel like you absolutely need to be in one of those three chapters though you may want to reevaluate why you want to join a sorority.

if you got cut it probably just wasn't meant to be. open your mind to other sororities. if other chapters who did invite you back are having spring recruitment give them a chance. just because they weren't your first choice doesn't mean you can't find a home there. the best piece of advice I got when I went through recruitment was to remember to look for the chapter who you are, not the one you wish you were. the sorority i joined wasn't ever in my top few, but i've grown to love my sisters.

when I went through recruitment, I felt similarly with where I ended up but also now love my sorority. I recommend you give both kappa and other sororities (SK, DPhiE, Signa) a try during spring recruitment. If you only like kappa, and don't get invited back, id give fall recruitment one last try with a way more open mind. I truly learned that I went through recruitment looking at sororities that were "top" and not necessarily the ideal fit, which is not advised at all.