First let me send out a shout to my first exposure to strong-but-sensitive men: Happy Birthday, Dad!
Now let's have a look at strong female characters. I heard (haven't been able to confirm) of an interview with Joss Whedon, the producer, director, writer, actor , composer, etc. who has contributed greatly to American pop culture. (Think Buffy, the Vampire Slayer, Angel, Firefly...) Supposedly the interview went like this:
Q: Why do you write such strong female characters?A: Because people keep asking that question.
I think that about settles the matter. In my case, I write strong female characters because I've always been surrounded by strong women and because I've tried to be one myself.
My female ancestors crossed plains in wagons, raised large families alone after being widowed, argued for female suffrage, and generally stirred things up. There is evening a somewhat apochryphal tale of a great-grandmother who found a bobcat on her kitchen counter and strangled it to death with her apron strings in defense of her sleeping baby. Wow.
I also write women because, being one, I see better through a woman's eyes, and I make them strong women because women can be heroes too, and often have been throughout world history.
For purposes of my plots, the women don't have to be physically strong. They, like my strong male characters, are willing to do what they fear in the defense of what they believe is right, challenge established belief, and pioneer defend the weak and helpless around them.
A few strong fictional women are currently inhabiting my head. I welcome them.