These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Soyogi didn't want to get close to Nagi because she doesn't care to end her life young. Karin desperately wants Nagi because she doesn't want him for to be murdered. Shizuku doesn't care about Nagi, and is just using him as a means to carry out the Rising Dragon Ritual murder-suicide.
As of chapter 116, it's revealed that Shizuku does in fact care for Nagi. Her suspicious actions earlier were part of a plan to kill herself, and only herself, so that everyone else would be happy. In short, from the very beginning she has been trying to manipulate events so no one but her can get hurt.