"Strong people don't put others down... They lift them up." -Michael P. Watson
Anyway. *clears throat* First of all:
Don't confuse strong character with a strong personality. Pushing everyone else around doesn't make you a strong character. It just makes you a bully. A strong personality is nice to have but you can have one and still be weak in other ways. And to be quite honest, I'm getting rather tired of all the strong personalities taking over in movies. It's beginning to feel like every single show has to have its own version of the Black Widow.
Here's the difference between character and personality: personality is something you're born with and doesn't change a lot except through severe trauma and/or brainwashing. Character can and does change. It's what you're like deep down--what decides whether you will fall apart or face it out when you're at the end of your rope. Strong character isn't about scissor kicking SWAT teams. It's about facing your problems even when you want to run away. Every hero or heroine has to do this in order to win.
A strong character doesn't have to be better than everyone else. The great thing about creating a strong character is that you don't have to give her any special abilities. You can if you want to, but she doesn't have to be amazing. Personally, I prefer a main character who hasn't got anything special but just uses the ordinary stuff she has to be awesome. I wasn't born with amazing super powers or deadly accuracy with a bow--I wasn't even born with a strong personality (I'm a bit of a pushover)--and I like reading about people who are like me.
A strong character doesn't need to be respected. If you are strong enough to stand for what's really important, you'll usually find yourself alone. If you were a weak character you'd be standing where it's easy--where everyone else is standing. People don't often respect what they don't like. If you're standing up for something they know deep down they should be standing for too but they're not, they won't respect you for it--they'll hate you. A strong character doesn't need to be respected because it's not about her. She didn't make her choice because she needed an ego boost. She made it because it was the right thing to do.
I put "female lead" in the title of this post because I thought it might make more people read it, but actually these points are true of both female and male characters. A strong character could be a guy with tats or a girl in frilly dresses with a parasol. It's not about what's on the outside. It's about that solidness inside the character that can't be crushed no matter what awful events the author dumps on top of her.
Don't believe me? Here's a few examples:
I'll be doing a follow-up post soon (hopefully) about Mary Sues and I KNOW I'll step on a few toes with that one, so stay tuned.