Are our hands really chiral? Everyone says that our left and right hand are mirror images of each other and are non-superimposable, unlike a sphere whose mirror image is exactly superimposable. But shouldn't our left and right hand be considered achiral?
If I move my hands in front of me such that palm of both the hands face towards me and move my say left hand horizontally such that it can be superimposed on the right hand clearly they can't be because the thumbs point in opposite directions.

But if I rotate my left hand by 180 degrees so that now the palm of my left hand faces away from me then both the left and right hand are superimposable. So shouldn't they be achiral? I know there are two more similar questions akin to this but none of the answers answer my simple question.
Holding your hands in this way merely proves that your hands are mirror images. If you take any object (chiral or not) and hold it up to a mirror, you can always align common features.

Imagine instead placing one of your hands inside the other. You may be able to align the overall thumbs and fingers, but they will be facing opposite directions, thus are not completely superimposable.

If you'd like further confirmation that your hands are chiral, try shaking someone's right hand with your left. Or try putting a left hand glove on your right. The interaction of mirror image forms (enantiomers) of a chiral object (like your hands) is different with the mirror image forms of another chiral object (like a glove or someone else's hand).