At that age, I don't think Nanami really came to grips with the fact that she was killing the kitten, just that she was getting rid of a barricade between herself and her brother, but others in this thread have addressed that complaint better already, so if reading their comments won't change your mind, mine definitely won't!

I always saw Nanami as a foil for Utena.  In episode 17, Juri and Akio both talk about pain caused by innocence, and I think Nanami carries this the best.  She wants people to suffer humiliation, but she's completely innocent of the notion of suffering.  In a way, she's aware that she's cruel, but just how deep it goes is beyond her, especially when she's innocent of meddling.

This changes later in the series, of course, and I think the turning point for her is really when Tsuwabuki talks about adulthood.  By the way, can you say masterful?

She also shares Utena's stubbornness, and the Cowbell episode is my favorite for that.  Nanami sticks to her own principles without realizing her own naivete, and to pit Utena against her at every turn shouldn't be over-looked (Don't compare that to my clothes!).  Utena really has no idea what she's doing either, which is why Anthy gives her the red sweater.

All these similarities make diru's point very plausible.  I only wonder whether Nanami would be capable of forming a close bond with Anthy, given that she's completely jealous of her.