Honestly this is a solid question and I feel the answer will be a bit lackluster. The TL:DR of it was that Collins was "up" in the rotation and Deke Slayton, who ran the astronaut office, made a call. The longer answer is a bit interesting too, though.

So if you'll recall, the US responded to the Soviet space launches with an announcement of Project Mercury, led by their intrepid crews of astronauts (star sailors). This first cohort was required to have jet aircraft experience as a prerequisite, as that meant they were already familiar with flight systems, high-altitude maneuvering, pressurized suits and oxygen tank systems, etc. These were the men of the Mercury 7 -- John Glenn, Alan Shepard, Wally Shirra, Deke Slayton, Gus Grissom, Gordo Cooper, and Scott Carpenter.

But there were only 6 Mercury flights. What happened?

Well, it turns out that once NASA started pokin & proddin these guys, they found that Deke Slayton had a medical issue with his heart, nothing serious but enough to have him grounded. As a bit of a concession, he was chosen to be the head of the astronaut corps, in charge of overseeing their wellbeing and most importantly, the flight order and crews. Since he was still "one of the guys", at least moreso than any of the suits or engineers, he had a good feel about who would work well together, which people would complement each other's skills, and who may need more training.

He worked in this role well through the Gemini missions, watching the men he'd trained with go to space repeatedly without him, and when Apollo came around he had a whole new cadre of recruits to sort through. The first mission, Apollo 1, was to be flown with one of the original Mercury veterans, a Gemini pilot, and a rookie Apollo pilot so Deke chose Gus Grissom, Ed White, and Roger Chaffee. That crew met an untimely and terrible fate during a rehearsal of their launch, and a number of missions had to be pushed back during the 2-years of research and redesign before it was safe for crews again. In that time Deke got to know the new guys and missions started getting handed out. There'd be no Apollo 2 or 3 - those missions could be made redundant with Apollo 4 & 5 after the additional time for testing on the ground. Apollo 6 would be an uncrewed test of the core systems, and if all went well Apollo 7 would be the first crewed mission after the fire. Deke went with the same plan as before, with Mercury vet Wally Schirra leading the new guys Cunningham and Eisele.

But before that mission got off the ground, the next couple of missions were already being trained for and had to have crews set aside for them. Now I should mention that there was always a backup crew who was responsible for learning everything about the "prime" crew's mission so they wouldn't have delays if anyone couldn't fly. This was important, as there had been accidents involving astronauts in airplane crashes (C.C. Williams, See, Basset, Freeman... Collins mentions something like 7 died in one year alone due to the amount of flight hours they were putting in). But once that prime crew lifted off, you were on the top of the list for next available mission -- usually that meant 2-3 missions down the line so you had enough time to train. So for the Apollo 8 mission, Deke had selected Frank Borman, Bill Anders, and Michael Collins to lead the prime crew. Borman and Collins had already seen time as Gemini pilots, so it was up to Deke to select who would be in command and he went with the more stoic Borman, with Collins as the Lunar Command Module Pilot. His training was cut short, however, when he developed a herniated disk in his back and had to have surgery. This meant his counterpart in the backup crew, Jim Lovell (of later Apollo 13 fame) stepped in as his replacement.

Once Apollo 8 had flown, and it was clear that Collins was recovering fairly quickly, he was brought back into the flight lineup at the top and given the next available mission - Apollo 11, where he'd reprise his training as a LMP CMP. Now it's important to say that at this point, it wasn't clear if Apollo 11 or another mission would be the first to land on the moon -- all that depended on how well each preceding mission would go. They trained with lunar landing in mind, but were also training on Apollo 10 techniques (basically the whole landing minus actually landing) in case that mission wasn't a complete success. Once it was clear that Apollo 10 nailed it and the next step would be going to the surface itself, the crews and their roles were already in place and fully trained to go.

Hope that helps a bit. Like I said, it was a bit more of a "gut feeling" than anything too scientific. Though I should say Mike always had a bit of a fun sense of humor about those "scientific personality tests" anyways, having failed in his first astronaut application process because at the end of his psych evaluation he was shown a series of inkblots and the final one was a pure white paper. His response, he claimed, was the only reason he could think of for his rejection -- he said it looked like "two polar bears fornicating in a snowbank."

He was a special dude, and everyone in the astronaut corps loved his goofy personality. One of the greats, and an amazing author as well. Most of this response, in fact, comes directly from his book "Carrying the Fire" which is considered widely to be the best of the early astronaut memoirs. Highly suggested.