Why does cutting food the same size matter?
Because cooking is a rate, and pieces of different sizes cook at different rates — so uneven cutting guarantees that something is overdone by the time the largest piece is ready.
The physics. Heat moves from the surface inward, and the time for the centre of a piece to reach temperature scales roughly with the square of its thickness. Double the thickness and it takes around four times as long. A piece twice the size of its neighbour is not slightly behind; it is far behind.
What this produces in practice: roast vegetables that are simultaneously burnt and raw; stews where some potato has dissolved and some is hard; stir-fries where the onion is charred and the pepper is crunchy; and chips that are unevenly done throughout.
The corollary that is more useful still: cut different ingredients to different sizes so they finish together. A dense root vegetable cut small and a courgette cut large will arrive at the same point. This is how a single tray of mixed vegetables is made to work, and it is the technique most home cooks have never been told.
The other reasons shape matters:
Surface area determines browning. Smaller and more angular pieces have proportionally more surface, so they brown more and absorb more seasoning — which is why a rough-cut roast potato with plenty of edges browns better than a smooth one.
Texture and eating. Uniform pieces are pleasant to eat; the same ingredient in three sizes is not.
Cooking method compatibility. Anything cooked fast at high heat must be small and uniform, because there is no time for a thick piece to catch up.
Why professional kitchens are strict about it. Named cuts — dice, brunoise, julienne and the rest — exist so that any cook produces the same result and every portion cooks identically. It is a consistency system, not ceremony.
The practical rule: if in doubt, cut everything slightly smaller than feels necessary, and add fast-cooking ingredients later rather than cutting them larger.