Why did Adama think he could break the endless circle this way?

The Centurions had basically been the slaves of the flesh Cylons. Remember that the flesh Cylons were ready to "lobotomize" the Raiders (sentient fighters) so they would no longer defy them

S4E2: Six of One

Natalie: Something has changed.
Cavil: Thoughts have changed. Yes, they change. The Raiders changed. That’s where all this started, with them. Somehow they exceeded their programming, and unlike us, they can’t correct themselves. So we’re gonna have to do it for them.
Natalie: Do what?
Cavil: We’ll reconfigure their neural architecture, and shave down their heuristic responses.
Leoben: Dumb them down? Lobotomize them?
Cavil: They’re tools, not pets. But in any case, it has to be done.

The skin models freed them because it was the right thing to do, not because they were trying to avert another cycle. From S4E20: Daybreak

Ellen Tigh: We'll give the Baseship to the Centurions, let them find their own destiny. I think they've earned their freedom.
Romo Lampkin: And what if they evolve again on their own and decide to come back in a few hundred years and wipe us out?
Ellen Tigh: It's a risk, but I think setting them free may be enough to break the cycle of violence.
William Adama: Then it's a risk worth taking. And I agree. They've earned it.

The only way you can win beings with free will over that you may have wronged is to stick your neck out and have to hope your goodwill and actions have convinced the other side not to chop your head off. Besides, the remaining flesh Cylons were staying on Earth, and they were the ones who caused the atrocities in BSG.