Summary: The Doctor has a helping hand from nature when it comes to Rose and her pretty boys.
The Doctor's knowledge of all things human was vast, not to put too fine a point in it.
So vast, in fact, that he knew quite a few things about the species that they didn't know about themselves.
One of these things involved a pheromone. It didn't have a name, because by the time humans were intelligent enough to have any kind of understanding of such things, it had become obsolete – it no longer existed. It had existed amongst humans' early ancestors, however, and the Doctor had a particular interest in it.
All pheromones gave off some kind of message – a chemical message that could be picked up by another creature. It might be 'I'm afraid' or 'I'm on the hunt' or just good old 'I'm horny'.
This pheromone said 'I'm taken, and if you come near me, he'll kill you.'
He'd acquired a substantial quantity of it a while ago at an intergalactic market; if he'd had anyone else travelling with him, he probably would have passed it by, but no – he had Rose.
Rose, a young, pretty human girl with an astounding ability to summon all of the pretty boys in the vicinity, and then some.
It took far too much energy to scare them all off himself – he needed something that would eliminate any threat before it became a threat.
Hence the pheromone. He mixed it with her deodorant, her perfume, her bubble bath, her washing powder, her shampoo – anything and everything.
She couldn't sense it, but they could.
A pretty boy would wander over, showing an interest, and then wham! Blasted by the pheromone. While it didn't exactly paint the word 'taken' on Rose's t-shirt in neon colours, it at least planted a strong doubt as to her availability in the boy's mind. He'd cast a wary look in the Doctor's direction and scuttle off elsewhere. Problem solved.
Rose became quite offended; started to worry if she smelled that awful, which was amusing – to the Doctor, at least – because bathing just meant more pheromone.
Maybe it was wrong of him. He wasn't sure. Wasn't sure he cared, either. He hated always having to be on the lookout for someone who might one day sweep Rose off her feet and out of his life. She was his, for God's sake, couldn't they see that? He loved her and she was his.
Now. If only he could find a pheromone that would make Rose realise that.