At the beginning of Numbers 4, the Text splits into a separate discussion about the three sons of Levi: Gershon, Kohath, and Merari.
Curiously enough, the conversation starts with the second son, Kohath, instead of the older son, Gershon. This isn’t the first time a rearrangement in birth order has happened. In one of the first genealogies in Scripture, Shem is listed first (Genesis 5:32) despite Japheth being the oldest (Genesis 10:1).
Why Shem? Because that’s the line that Abraham came from, which is of premiere importance in the story of Genesis.
The exact same thing happens in Numbers 4. Kohath is listed first because its from his lineage that we get Moses (through Amram). More specifically to this Text though, we also get Aaron, who also comes from Kohath. That’s why he appears first.
But the the story in Numbers 4 doesn’t have as much to do with Aaron’s priestly line as much as it does his cousins, the Kohathites. These people were responsible for the most prized possessions of the Tabernacle: the table of the showbread, the lampstand, the trays, the oil vessels, and other “holy things” from inside the veils.
God is very specific with how He wants these things moved, though. He doesn’t want a moving van loaded up and the objects thrown inside; instead, He mandates two layers of material between the holy objects and human hands.
The Ark of the Covenant, for instance, is covered with the veil of the most holy place. Based off of Numbers 4:17-20, some Jewish commentaries argue that the priests were required to cover them even before this took place, arguing that the sacred items were only for the priests’ eyes.
There’s undoubtedly a level of mystery and wonder that’s put into these regulations. Why else would God want them shrouded before they’re moved from place to place?
The argument then goes that human eyes are not to gaze upon the infinite. If idolatry is the act of humanizing a deity to fit our standards, then it follows that covering up the items does the exact same thing in reverse. The average Jew is forbidden from seeing the items in order to keep the scale of God as large as possible.
Regardless, the Kohathites were given a choice position, even if they weren’t the ones directly interacting with the sacrifices. It also shows that there’s order even in the smallest of things—like how to practically transport the worship of God.