Steller was a naturalist, but he accidentally encountered the animals while on an expedition that had become lost and ravaged by scurvy. They'd run aground and assumed they could walk to Siberia (if you're ever longing for the comfort and safety of Siberia, something has gone horribly wrong), but Steller soon realized they were on an island that had likely been untouched by humans. Then he spotted the sea cows.
Steller had two reactions to discovering the behemoths. The first was that they were majestic wonders of nature, and the second was that they were stupid and delicious. One of the 10-ton beasts could feed the crew for a month, and apparently they made for some damn fine eating. Their reaction to being harpooned was to sort of float there and take it, with other sea cows ineptly trying to mount a defense, and even making themselves vulnerable by returning to visit the corpses of their mates.
The explorers were eating to survive, but Steller envisioned a future in which hunters could come to the island and live off the cows, while harvesting both their fat and valuable pelts from the island's countless otters. And that's pretty much exactly what happened, with fur hunters driving the sea cows to extinction. They were already in rough shape, with only an estimated 1,500 still alive at the time of their discovery. The nonstop harpoonings of the poor placid bozos didn't exactly help, but the real problem might have been the mass otter hunting, which lowered the number of sea urchins being eaten, which let the urchins consume more kelp, which starved the cows of their main food source.
This annihilation wasn't callous indifference. Steller and most of his contemporaries believed that nature was inexhaustible, and would keep spitting otters and sea cows at them no matter how many were slaughtered. So if there's an upside to this story, it's that this case made everyone re-examine that belief in a real hurry. The concept of extinction became a part of natural science, and the sea cows have also contributed to an understanding of how over-hunting can affect species. So could someone go ahead and Jurassic Park these pitiful bastards back into existence, please?