I keep a running list of everyday words that turned out to be stranger than I assumed, and "fathom" sits near the top. We use it two ways without blinking. A fathom is six feet of water. To fathom something is to understand it. Those feel like unrelated words that happen to be spelled the same. They aren't. They're the same word, and the thing connecting them is your own body.
It starts with Old English fæðm, which meant your outstretched arms. Not a number, not a tool: the literal span from fingertip to fingertip when you spread your arms wide. For an average adult that span runs about six feet. That is the whole reason a fathom is six feet. Somebody measured it against their own body, and the measurement stuck. The deeper root reaches all the way back to a Proto-Indo-European sense of "spreading out," the same family that hands us Latin patere, "to lie open," which is where we get "patent."
How it got wet
The nautical part comes straight out of that bodily image, and more literally than you'd guess. Sailors measured depth by dropping a weighted line over the side and hauling it back up hand over hand. The natural way to measure the rope as it came in was by the armful: spread your arms, gather a span, spread them again. Each armful was, quite literally, one embrace. One fathom.
So the unit isn't some abstraction a committee dreamed up. It's your spread arms, repeated down into the water.
How it got into your head
The verb grew out of the same motion. "To fathom" first meant to encircle something with your arms. Then it slid into "to take soundings," to measure the depth, to find the bottom. And then English did the thing English loves best: it took the physical act and made it mental. Getting to the bottom of the water became getting to the bottom of a matter. By the early 1600s, to fathom something meant to penetrate it with your mind, to understand it all the way down.
"Unfathomable" is the perfect fossil of the whole chain: water so deep your line never touches bottom, a mystery you can't get to the bottom of. So the next time you say you can't fathom someone's reasoning, you're reaching for a four-hundred-year-old sailor's metaphor. You dropped your line and never hit the seafloor.
The cousins keep the older meaning on file. German Faden now means "thread," but it was once that same arm-span measure. Old Norse faðmr just meant "embrace." Somewhere underneath the navigation and the comprehension, the word still means exactly what it always did: your two arms, open wide.