To understand why cooking is a chemical change, you should first understand what is a chemical change. Basically, all changes in this world can be classified as either physical changes or chemical changes. The difference is that chemical changes bring about new substances while physical changes don’t. Take the example of baking: when you bake a cake, the most immediately observable change is that it expands. This is because the baking soda in it has undergone a chemical change under heat to release carbon dioxide. Notice there is no carbon dioxide in the cake before we bake it. That is what I mean by bringing about new substances.
If we break down the art of cookery, it basically aims at altering either the texture or the taste (or both, as in most cases) of the raw materials. And to achieve that, the raw ingredients almost always must go through some kind of chemical changes. To be sure, although making your cake fluffy through baking is indeed a chemical reaction, some changes of the texture of the food might not involve chemical changes: you don’t create any new substance by mashing the steamed potatoes. But changes in the taste are always chemical in nature, because the process of tasting itself is a chemical reaction between the food ingredients and the taste buds on your tongue. For example, when you toast a slice of bread, it becomes carbonized, meaning the carbohydrates in the bread break down to carbon under high temperature. That is where the slightly bitter taste comes from.
So why is cooking a chemical change? Because almost all cooking methods involving the rise of temperature (which is basically to say, all cooking methods) involve chemical changes. Once under heat, the antioxidants omnipresent in vegetables will get oxidized and the proteins in meats will get denatured. Among other things, the former process will mostly result in the change of color of the vegetables, and the latter the stiffening of the meats.