"Alpha" or "omega," while they can mean a lot of things, in this case refer to personality types. They are primarily used when talking about "pack" animals such as wolves. Let's use the example of wolves: an "Alpha" male, female, or pair would be the wolf that the pack follows. The alpha is the leader, the dominant one. "Omega" is taken to mean the exact opposite -- one who follows unquestioningly. I'm guessing "Beta" would be someone who falls in between these two extremes.
I disagree with freethinker on this one. My husband and I are very Alpha...we're very stubborn, almost bullies, and we have our own ideas about how to run the show. We are most definitely not followers. We are subordinate to no one. (You should see us when we argue!!)
I think childfree in general come from all walks of life so it's hard to say whether "most" would be a certain way. Some childfree may that way because they are alpha -- I know I am a rebel, I don't want to follow "the script" that mainstream culture has set up for people. I want to be my own boss and create my own path, and take as many people with me as I can (i.e., convincing them this is a good way of life). Others may wish to be childfree because they are "omega" -- they feel uneasy about making all the decisions for another person's life, as a parent has to do for many years of a child's life. They don't want to call the shots or deal with the horrors of disciplining someone else, when they are unsure of themselves.
Perhaps childfreedom is simply a preference that has less to do with one's leadership qualities and more to do with one's personal comfort and the boundaries and norms we all set for ourselves.