So, I have a character who has an interesting quirk: they cannot wear flat shoes or boots (i.e. where the heel is at the same level as the ball of the foot or approximately so, within 1.27cm or so) without risking pain/injury to their feet and legs. What sort of physiological trait or "defect" would cause this in an otherwise normal human being? Said trait can be heritable or idiosyncratic, but needs to be present from birth or young age, should not interfere with their ability to walk/run when suitably shod, and should not affect the appearance of their feet in any clearly noticeable way.
It's a relatively common problem but possibly off-topic for world building
Over time, wearing high heels can shorten the muscles in your calves and in your back, leading to pain and muscle spasms
The effect is that it's painful to walk in flats.
You could cause someone to be born with this, though it would normally be treated medically rather than through wearing stilettos.
I'm not too hot on biology: but the first thing that comes to mind is a shortened Achilles tendon/tendon assembly in the ankle. This would lead to this person's natural foot position being a 'point', and wearing flat shoes would be intensely uncomfortable (ever tried pulling your foot up as hard as you can? Remember the stretch in your calf muscle?).
The issue here is that tendons and muscles change through use. Wearing flat shoes for a while (though unpleasant) would resolve this issue by literally stretching the appropriate parts of the body. If the physical defect also affected the strength/flexibility of the muscles and tendons, leading to severe damage if they were stretched, then this person would have to wear heels all the time. They would also completely cripple themselves the first time they turned an ankle...
A claw-like foot. The hands and feet of people with ectrodactyly are often described as "claw-like" and may include only the thumb and one finger (usually either the little finger, ring finger, or a syndactyly of the two) with similar abnormalities of the feet.