And yes, the Torah is constantly, through many mitzvos, asking us to be above normal humanity. We can’t eat whatever we want, even though naturally we would. We naturally wouldn’t take a day every week to acknowledge Hashem’s control over our livelihood and the world itself. We wouldn’t refrain from wearing wool and linen.
The medrash asks why Hashem cares where a cut is made on an animal for it to be kosher, and answers that it’s “letzaref es habrios” to purify people, for our benefit, to elevate us above “normal” humanity into something special. Something malaachim are jealous of.