Humans have nothing like a generation ship set up on Earth
I disagree. The Austronesian people colonised the Pacific Ocean by this means and handled it just fine for three thousand years before the arrival of fast steamships and radio put a close to their isolated lifestyle.
An island isn't outer space.
There are still some small, isolated human groups with only a couple of hundred individuals.
The Sentinelese people of the Andaman Islands in the Indian Ocean are completely isolated from the rest of humanity, and some estimates put their population as low as fifty. They still retain sufficient sanity to understand that missionaries are best killed on sight.
Isolation from people isn't as much the issue as isolation from the environment itself. Living in a tin can forever, we aren't exactly wired for that. And while we can choose who starts that process, the generations afterwards might not be able to handle it as well. Granted, it would be all they know, so possibly could work.
Just because currently spacecraft are all 'tin cans' with no life other than the astronauts and perhaps a couple of experimental plants or animals, and no room to swing a cat even if one was brought along, doesn't mean that it will always be thus.
Which then leads to the next issue.
Generation Three said:
"Why are we doing this?! If we turn around now, we can get back to Earth quicker. We're so sick of eating sausage."
A generation ship would likely need an ecosystem, rather than a mere life support system - after all, that's how spaceship Earth has managed to support life for thousands of millions of years without a service call to the maintenance department.
My gawd... hogweed eventually becomes the sustainer of human life in space. The irony.
A generation ship would have to have more in common with a remote island than with the International Space Station.
I can't imagine how many generations we'll need to create a generation ship. In the end, a generation ship's benefit is limited. I mean, other than in the Wall-E sense of things. The commitment to the mission is tenable with each following generation. And I ponder just how large a crew is needed to make it work. The redundancy for the ship equipment would also be needed for the crew, engineers, doctors, mid-level accountants, justice, sanitation engineers, people that know why that blue button keeps blinking all the damn time, botanists, biologists, physicists, chemists, computer experts, someone that can fix musical instruments, educators, and one libertarian to fuck it all up. In general, novels and shows usually have one or two people do all of that stuff, but it isn't really possible.