People have been throwing the phrase 'strong female characters' around for years now, and yet there still seems to be a lot of confusion about what it means. So just to add to the melting pot of misapprehension, here's my contribution to the debate. Because as far as I can tell, there are two very fundamental aspects of the phrase that contribute to the general crossing of wires.
1. The word 'strong'
It's natural to assume that 'strong' means 'physically strong'. So a whole bunch of writers see the demand for 'strong female characters' and think right, all we have to do is write a woman who kicks ass. But that's not what strength means, not really.
First of all, there are hundreds of ways to be strong. Why prioritise one (traditionally 'masculine') strength – the ability to wipe the floor with someone in a fight – over all the many other kinds of strength out there? Compassion is a strength. So is endurance. So is forgiveness. Not being able to defend yourself against a more powerful assailant doesn't make you a weak person. Nor does asking for help. I realise we want to get away from the 'damsel in distress' who sits around waiting to be rescued, but that doesn't mean all women have to be able to slay their own dragons. After all, not all men can. What we really want to see in our characters, I think, is inner strength – and that's not the same thing at all.
Second, a really strong character isn't a perfect one. Which is why, again, the word 'strong' is completely misleading. A character who was nothing but strong – albeit in the varied ways I mentioned above – would be a bad character, because she would have no room to grow. It may seem paradoxical, but strong characters need weaknesses. And not just tacked-on faux weaknesses like 'clumsiness' or 'perfectionism', either. Real, honest weaknesses that give a character's inner strength a chance to shine through a gradual process of self-awareness and battling to overcome her own flaws.
So what we're really looking for isn't strong female characters – it's well-rounded female characters. Which brings me neatly to point 2.
2. The word 'female'
In my opinion, the focus on 'female' in 'strong female character' is another huge mistake. Which isn't to say that we don't need well-rounded female characters – of course we do. But by focusing on the 'female' specifically, the entire debate is framed under the basic assumption that writing good female characters somehow takes a different skillset than writing good male characters. George RR Martin says it best in this respect (I'm sure you've seen this plenty of times before, but I'm going to include it anyway, because it rocks).
The question shouldn't be 'why aren't writers writing well-rounded female characters?' It should be 'why are writers investing any of their characters (male/female, black/white, gay/straight, disabled or not, human or otherwise) with less than full personhood?'
There are a couple of possible answers to that question. One is that certain characters exist only as plot devices – they are there solely to allow the protagonist to achieve his goals. I say 'his' because in a certain type of spec fic this tends to be the case; the protagonist is male, and the female character is there to help him grow and reward him with herself at the end, without having anything like a fully developed inner life of her own. But male characters can also be plot devices. I've read plenty of romance novels where the male lead is a blatant attempt at wish fulfilment and, therefore, no more than a cardboard cutout.
Another possibility is that certain characters have been included as tokens. This is basically the lazy writer's attempt at diversity. Often this kind of character appears in a narrative because, y'know, people have been talking a lot lately about how there aren't enough characters of type X in movies, so hey, I'm gonna put one in my latest screenplay. The writer pats herself on the back for being 'diverse' and including 'variety', but doesn't bother to go beyond a stereotype. It's as if just labelling a character with some broad-stroke designation is enough. And to be honest, that's almost more offensive than ignoring the existence of certain groups: the idea that no further characterisation is needed for this particular character because he's Asian or bisexual or in a wheelchair and that's what defines him.
We're getting a little far from the point here. The need for more and better diversity in books and films is another topic entirely, and I certainly don't claim to have achieved it in my own work. (I know very well how easy it is simply not to notice the fact that one's characters, no matter how different and interesting and well drawn they are, are set very firmly within one's own sphere of experience.) So let's leave that for now, and return to our so-called strong female characters.
My point here is that the phrase is both misleading and limiting. I think what we all actually want is for the characters we watch and read about to be three-dimensional, no matter what kind of characters they are. Writers shouldn't be fixing on a particular kind of female character with a particular kind of strength. They should simply be focusing on making all their characters as realistic and well rounded as possible, without drawing on stereotypes or making assumptions. Writing a 'strong' woman requires exactly the same skills as writing a 'strong' man; same for sexuality and ethnicity and disability and even species (because not all dwarfs have beards). And in fact, the sooner we realise that people are people before they are whatever other definitions we apply to them, the sooner we might actually start to see more diversity in fiction, because we won't be afraid to venture beyond the boundaries of our own experience. We will simply write each individual character as just that: an individual.