I am notorious for coming down hard on female characters, especially in pairings. I can admit it. However, a lot of this doesn't really stem from me looking for a "self-insert character" to project on, or the desire for the classic "relateable female lead" that was mentioned earlier. Here's my take on the matter.
In general, a lot of video games (and anime) are targeted primarily towards men, or towards a broad audience but with the underlying assumption that men are going to be the most likely to buy into the series. As a result, there are a lot of instances in which the female characters are written in such a way that they appeal to men, but don't necessarily appeal to women. I get it; it's an industry, and you need to cater to the needs and interests of your clientele. There's nothing wrong with this.
However, as a female, it get's really debasing after a while when the pandering becomes blatant, and it makes me increasingly more jaded and scrutinizing of female characters. Are they actually a good character? Are they motivated? Do they assist the plot at all? Are they a sexual character or a sexualized character? In the end, I tend to spend a lot more time analyzing the merits of the female characters, or rather, the female side of the pairing equation as opposed to the male side. Seeing that I am a female, I think that this makes sense. It's a lot easier for me to see when a female character is being used as a tool in the same way that men can fairly easily identify weak, pandering male characters.
For the record, I'm not generalizing and claiming that all female characters suffer from pandering or poor writing. Far from it, actually. And on the flip side, I acknowledge that there is media aimed at women, and it reverses the situation in such a way that the men are the idealized forms and have been crafted to appeal to women, which makes actual men cringe. In this sense, it evens out the playing field a little, and it gives me greater context and understanding when I see media that panders towards men. As I said, you have to appeal to your audience, although I believe it's much more advantageous to it in a subtle manner.
In short, shipping is contingent on liking both characters in the pairing. Since the majority of shippers seem to be women, it's natural that female characters are going to be examined a little harder, because that's what fangirls can quickly identify with or reject. (I think the same would be true if the majority of shippers were men. We'd have fewer arguments over the ladies, and more arguments over the merit and plausibility of manly tears and excessive shirt-removal.) This is compounded by the fact that there's a slight but undeniable sexual bias that tends to favor men and do an occasional disservice to female characters. When a fangirl fails to find a suitable female partner for her male character of choice, this is when the floodgates open up and male/male pairings start to enter the equation. (Speaking purely from my own experience and observation. Again, not generalizing all fangirls here.)
I would also like to mention that FE has some exceptional female characters, in my opinion.
Except for Ninian. 8D