Why do I have difficulty squatting with my feet flat on the floor?

What I mean is squatting like this:
http://farm4.static.flickr.com/3341/3344342095_ef32fee239_o.jpg

Notice that her feet are flat on the floor and her legs are tilted slightly forward to help balance the weight of her body. Also, her feet muscles are quite relaxed, without any obvious strain.

That's exactly what I have trouble doing...

Whenever I try to keep my heels on the floor when squatting, I always end up falling backwards due to the weight of my bottom (since I weigh 105 pounds and have a BMI of 18, I'm obviously not heavy... quite the contrary).

I notice that unlike the girl in the photo, my legs cannot make that 80-degree angle with my feet. They're stuck at a 90-degree angle and when I try to push them forward (with my back against a wall), my muscles feel very strained and sore.

I've also tried spreading out my legs a little, but then my legs cannot make contact with my thigh, I can't lower myself below a certain point, and it feels more like "suspended sitting" rather than a squat.

So... why can't I squat with my feet flat on the floor? Why can't I make that acute angle between my legs and feet? Is there something wrong with my muscles?

Thanks!