Kelly Starrett has a great video (short, to-the-point, and not overly technical, unlike most of his stuff) that talks about how to buy shoes for your children—the advice is equally applicable to adults as well.
Early on, he says:
We’ve been evolving for two-and-a-half million years, and you’re evolved to have your heel flat on the ground.
This is an important point to consider. The body adapts to the stresses placed upon it; this is a basic tenant of exercise science, physiology, and basic biology. For decades, we’ve been walking around in shoes with heels upwards of an inch (if not more) in height. Our achilles tendons adapt to this; they realize that they don’t need to be as long as they’re meant to be (since we’ve been buffering them with added heels) and systematically shorten over time.
Consider standing barefoot with your feet together, pointing straight ahead. Now squat to the ground, keeping your heels on the ground. Ninety-nine percent of you can’t, and you’ll find that you can only do this by bringing your heels off the ground. This is the same mechanism.
Another point Starrett makes: children almost always start to heel-strike while running around the 1st grade mark. In kindergarten, children run on their forefoot, and can squat like a human being; by 1st, they can’t do this anymore. He theorizes this is because parents start putting their children in fashionable heeled shoes, increase their sitting time (desks in kindergarten, anyone?), and beginning this maladaptation process early on.
These are all bases of our recommendations for barefoot running, barefoot walking, and decreased sitting time.
Starrett also has a nice video on his website about why you shouldn’t swing your kids by the arms.