Responding to a question posed in Doctor Who Magazine (via DoctorWhoTV), Steven Moffat explained that Doctor Who appeals to both boys and girls, and while the show stars a man as the eponymous protagonist, no matter what the regeneration (for now), he believes that the story has been about the companions, who have primarily been women. To that end, he doesn't want to damage Doctor Who by not having that "voice and viewpoint" represented. He continued:
Science-fiction is notoriously male. You can tell that because everyone wears uniforms and marches around talking about rules. But Doctor Who has always felt to me, rather female. It's full of kindness and compassion and eccentricity and wisdom instead of violence. And from that point of view it is important that the main character, the Doctor's best friend, should be female. Someone will now pop up and say it's called Doctor Who, not Clara (or or Rose or whatever). Well, listen you, it's not called The Doctor either, it's called Doctor Who -- it's about that question and who's asking it.
Historically speaking, the ratio of male to female companions has definitely been more weighted for the latter, though given how the main protagonist has always had a male form, Steven Moffat's views on providing a female-focused story to follow along with make sense. As for the men who have accompanied The Doctor over the years, Moffat considers most of them to be "friends-in-law," citing Arthur Darvill's Rory Williams as an example. While that opinion is subject to debate regarding the classic Doctor Who era, the modern era's male companions certainly haven't received quite as much narrative attention as the females they were with.
Doctor Who has been providing bonkers adventures across time and space for over 50 years (albeit interrupted on television for a while), and most of the time, the eponymous Time Lord hasn't been alone when traveling. He frequently recruits someone from Earth to travel with him in the TARDIS, and most of those companions have been women. There have been male companions sprinkled throughout both the classic and modern eras, but current Doctor Who showrunner Steven Moffat believes that the main companions should always be ladies because it's important to provide representation for both males and females on the series.
Of course, then that brings up the long-suggested idea of having The Doctor regenerate into a woman, thus allowing more leeway with using a male companion and providing representation on both sides. Since that's not in the cards for now, maybe the show should try spotlighting regular companion duos again, like Rory and Amy or Rose and Jack (not the Titanic couple). With Broadchurch's Chris Chibnall taking over as the Doctor Who showrunner in 2018, maybe he'll consider doing that.