Actually flat shoes are better for your feet you just have to not heel strike as much. This is the whole principle behind Vibram FiveFingers and barefoot running. The idea is that instead of landing heel first which will cause you all sorts of problems, the foot actually works better if you land more towards the toes on the middle of your foot so that there is minimal pressure on the impact of the heel. The best way to learn is to try running barefoot and landing on different areas of the feet.
The foot in itself is an amazing shock absorber, it has been designed to work thousands of years ago when there were no shoes so ideally we don't even need to where shoes although this isn't always practical. Shoes like Oly lifting shoes are aweful for you because they will destroy what little range of motion you may have. They lead to shorter Achilles tendons by having a raised heel which also cripples ankle flexibility.
Anything with a heel, obviously the worst being high heels but I hope you guys aren't wearing them
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, aren't very good for you, just the same as things like Ugg boots tend to mean that the wearer relies on the high tops for ankle support. I'm sure there are loads of resources out there which are great if you are interested in further info
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Also, roysters: Bare foot is the best thing for deadlifting because it reduces the distance you have to move the bar. In powerlifting meets I have to wear deadlift slippers: