First date with a girl? Of course! Bring her to the end of her world.
It makes a bit of sense. The Doctor is fresh off the Last Great Time War (we don't quite know it yet) and just watched Gallifrey burn (and we find out that at the end of the episode). Rose is running with the Doctor now, and he's an emotional mess, drowning in survivor's guilt and wants to make her be able to some how relate to not having a home planet any more. Its not quite the same as it being gone forever, because Rose will, of course, return to Earth. But I assume watching your planet, your home, you childhood, burn is watching your planet burn.
One of the guests is The Adherents of the Repeated Meme. They're not talking about those things on tumblr (ours is here). The original definition of "meme" is an idea that is passed from person to person through culture. Personally I think Clara is a living meme. I guess she gets Adherents. I know its them that let out those mechanical spider things, but who ever said Clara was good?
I give you air from my lungs!
STEWARD: And last but not least, our very special guest. Ladies and gentlemen, and trees and multiforms, consider the Earth below. In memory of this dying world, we call forth the last Human. The Lady Cassandra O'Brien Dot Delta Seventeen.Then, there is the second time we see the Doctor's survivor's guilt, after Rose has realize how much of a complete stranger the Doctor is and really starts asking him where he's from: "This is who I am, right here, right now, all right? All that counts is here and now, and this is me." He knows his past, and what he's done, that he let his planet burn exactly like the Earth is about to, and can't bear to think of it now, even though he is sort of making himself think of it given where he is and what is about to happen.
CASSANDRA: Oh, now, don't stare. I know, I know it's shocking, isn't it? I've had my chin completely taken away and look at the difference. Look how thin I am. Thin and dainty. I don't look a day over two thousand. Moisturise me. Moisturise me. Truly, I am the last Human. My father was a Texan, my mother was from the Arctic Desert. They were born on the Earth and were the last to be buried in its soil. I have come to honour them and say goodbye. Oh, no tears, no tears. I'm sorry. But behold, I bring gifts. From Earth itself, the last remaining ostrich egg. Legend says it had a wingspan of fifty feet and blew fire from its nostrils. Or was that my third husband? Oh, no. Oh, don't laugh. I'll get laughter lines. And here, another rarity. According to the archives, this was called an iPod. (Its a 1950s jukebox) It stores classical music from humanity's greatest composers. Play on! (A 45 of Tainted Love by Soft Cell.)