The Doctor has a dilemma, named Rose.
He's terrified that if he says or does the wrong thing she'll ask to go home to her mother and Mickey (neither of those two are anywhere near the top of his list of favourite people just now) and he can't risk that, can't risk losing the best thing that's happened to him since the bloody Time War. But, at the same time, he's very aware that if she does have feelings of any kind for him, and he doesn't give her an outlet to express them, he'd get good odds on her asking to be taken home anyway.
Either way, he loses.
So, what to do? he's thought of being less tactile - of holding, touching and (especially) hugging her less - but his mind recoils at that idea. He really doesn't want to go down that route unless he has no alternative. At the same time, he knows full well that that could easily backfire on him, too, as it isn't like she'd not take that as gospel truth that he doesn't like her in that way. And he's trying very hard not to do or say anything that could seem misleading or be misconstrued.
He just wants to be able to keep her - anything else would be a (welcome) bonus but Rose staying with him is his absolute red line. He has to talk to Rose, has to find out how many of Cassandra's actions whilst in her body are indicative of what she herself might want to do with and to him. This, even to him (a Time Lord, clueless about how humans operate in these situations), is blatantly obvious.
So.
Stuck between the rock and the hard place really, aren't we, Doctor?