Nekomonogatari White continues, but I think this time this will be quite short (Like it has always been when I say that)
Surprisingly Complex: M.S.S.S Episode 2
Okay. The Tiger is an outside apparition that is causing harm to Hanekawa for some reason. Coming from the matters discussed in this episode by Senjougahara, I'd say the Tiger comes either to those with a strong sense of fatalism (Everything that happens must happen), or to those with strong emotional detachment. Even though the missing chapters are confirmed to be the Cat taking over and we see the Cat talking to the Tiger, the main point of the episode is Hanekawa's mentality, and we will talk about that. Also, I'll explain why Senjougahara wanted to shake hands with the Cat.
Quicknote: Why all the close shots on Senjougahara when they were taking a shower? Hanekawa a bi? Possibly, as she probably looks people totally non-subjectively.
So... Hanekawa has a strong sense of fatalism, seen in Nekomonogatari Black, and seen now again. She also has total emotional detachment, or more like, total non-subjectivity. She doesn't eat food based on taste, but out of need to eat food occasionally. She also wears the bare minimum of what could be called clothes (Not in the skin-showing sense, you perverts) and buying what Senjougahara sees practically as rags, as they are clothes only really poor people would use. Not wearing clothes that look nice, wearing any clothes because society says you can't go around walking naked. But all the attire she has are approriate for the situation, so she doesn't go walking around in her pajamas all day. The Cat being a total polar opposite, goes walking around in pajamas all day, and wears even the pajamas only because the Mistress says that something must be worn. Hanekawa also puts no flavoring in her food, making it bland, but it doesn't matter to her as she only does food for herself. The only part she has some kind of attachment to life is people, as she finds Senjougahara's quirks slightly annoying.
In the first scene, before the opening, we almost hear Hanekawa's reason of loving Araragi, though, interestingly, we already did. Hanekawa does everything because it's normal. Araragi is a change to that normal, as he's some kind of a delinquent and doing generally what he pleases. It's kind of an wonder that to both Senjougahara and Hanekawa, the main reason they like him is change. The difference is, that with Senjougahara, it comes from making the change, where as Hanekawa is seeking for change.
And why is Senjougahara insistent on shaking hands with the Cat? Because she wants to know the other side of Hanekawa as well. The most probable reason for this is to get closer to her, so she won't do can't/won't do any drastic measures to pull her and Araragi apart. She's also curious, so why not?
Hanekawa may be bi? Also fatalism.