1. The Out-Of-Universe Evidence
The Doctor and his companion travel around the galaxy, alone, in dangerous situations, while living in the same relatively small space. The Doctor is a man, his companions are attractive women. Not addressing the idea of a romantic relationship is ridiculous. So why havent they, with Clara? Rose had a boyfriend for most of her time on the show. Not long after they broke up, she and the Doctor reached a breaking point where they confessed their feelings. Martha had no boyfriend, and Im pretty sure she never even had any one-shot love interests: she was just hopelessly in love with the Doctor, something she said several times. Donna said in her first regular episode that she was really, really, not interested in a romantic relationship with the Doctor. She and the Doctor regularly denied that they were involved, loudly, and for a disproportionately long time. Amy had two love interests introduced in her first episode (remember that guy? The one with the laptop?), came on to the Doctor, and thereafter rarely appeared without her fiancée/husband. So why hasnt Claras love life been addressed? This cant be the blockbuster format at work: Rose and Donna both had stand-alone love interests, and the Doctor has had a few. But shes never mentioned a boyfriend, a date, or anything of that sort. The family Clara works with thinks the Doctor is her boyfriendthe younger kid says things like thanks, Claras boyfriend, and neither Clara nor the Doctor bats an eye. The father Clara works for is comfortable enough with the Doctor that hes (unwisely) willing to leave his kids with the Doctor while Clara sleeps. The Doctor and Clara even have pre-established evenings when he comes to take her on an adventure.
Even if Clara and the Doctor werent giving each other looks, the Doctor clearly occupies the place in her life a boyfriend would. If theyre not a couple, they might as well be. Conclusion: "The world doesn't end because the Doctor dances." Look, Im not arguing that Clara is the love of the Doctors life, or that they should get married and have kids and River should stay dead because of them. Im just bringing together moments of subtext and text, and laying out the evidence. Maybe Im completely wrong, or maybe the writers will decide they want the next Doctor to be a woman and try to backtrack all this. But seriously, this particular love story is reaching the screamingly obvious stage where someone is going to have to talk about it onscreen. Bring on the 50th!