A binary choice is a choice with two options. Most binary choices aren't. For example "boxers or briefs?" is presented as having two options, but in fact there are others, such as going commando or wearing long underwear.
There are a lot of binary choices out there, like disciplining your children or spoiling them. Being permissive or harsh. Being left or right wing. Believing certainty, or that we don't know anything. Believing in God, or not. A child sharing his toy, or being selfish. A mother making her child share, or permitting him to act badly.
Each of the above examples isn't really a binary choice. There are all sorts of alternative options. For example one can be neither permissive and negligent, nor harsh in a variety of ways. One way would be to be helpful. This avoids "letting" kids do whatever bad things they want by helping them find out what is good to do. It also avoids being harsh by helping the child to get things he wants instead of thwarting him.
Common preference finding and non-coercion don't function in a world of binary choices. They involve creating new choices just as much as finding ways to like things other than our initial preference. Frequently, none of our initial solutions are good enough, and we need to think of new options.
If your child doesn't like something, do not tell him these are the possibilities, and that's the way it is, and he can have whichever color toy he wants as long as it's red or black. Buy some pink paint. If he doesn't like the options that seem to be available, it's time to brainstorm. Be optimistic.
Logic. What a concept.
I posted a filthy lie today.
another name for this would be false dichotemy