That's a hard one, because there are so many answers that are "right" for different people.
For me, I think the "right" time to butcher any cockerel is when I have a bit of spare time, or when I get tired of having him around, whichever comes first. That might mean he's crowing more than I want to hear, or fighting with other cockerels, or attacking people, or there are too many cockerels trying to mate with the hens, or I just want to reduce how many chickens are in the pen so the others have more space.
I find it helpful to remember that some people eat quail, and most cockerels are bigger than quail by the time I can be sure of their gender. What size is "big enough" to butcher is different depending on who you ask.
Chickens grow fastest at first, then slow down but continue growing for quite a few more months. Some keep growing for more than a year before they completely stop. The older they get, the more pounds of feed it takes to produce another pound of meat. They are also the most tender when they are young. If you want tender meat and the best feed/meat ratio, it's usually best to butcher them early (6-10 weeks).
But it takes about the same amount of your time to butcher one bird, no matter what the age or size, so butchering them at older ages means you get more meat for the hours you spend butchering. (If you choose to use different methods for different sizes of birds, that can change the per-bird time, but figuring that they all match is close enough for rough planning purposes.)
If you are trying to get the most meat per hour of your time, don't forget the time you spend tending them each day. If they are living in a separate pen, that can add up fast. But if they are sharing a pen with other chickens you intend to keep anyway, they may not take any more of your time each day.
If you've never butchered any before, you might want to butcher one as soon as possible, then think for a bit before doing any more. You will almost certainly learn a "better" way to do part of the job after you've done it once. (There are many "best" ways to do anything with chickens, and butchering is no exception.)
