Earlier quoted context omitted.
As you have invited personal criticism: You are naive and your thinking is simplistic. You have managed to get away from complete naivete, you think using abstract concepts, which allows you to look through the superficial appearance of things, and thus cut through a lot of bullshit. But you haven't noticed yet that your abstractions are way too abstract to give a reliable representation of the real world by themselv…
This a wordy and intellectually sounding repudiation of reason, nothing more.
Your logic reasoning skills may be pretty good, which is a component of reason that many people lack. What you seem to lack is a useful mapping between reality and propositions. And from false premises, unfortunately, even flawless logical derivation cannot produce any useful information about the world.
When wwweston critizes your black-and-white thinking, he is not suggesting (I think) that there is some kinda-maybe-not-quite-true-or-false truth value. Rather, he suggests that the choices you are implying actually have more than two mutually exclusive possibilities. In particular, words don't actually have "real meaning", words routinely have tons of meanings, heavily depending on context, which is why you cannot make a simple binary decision as to whether something is or is not an X. It's somewhat unfortunate, as that leads to lots of confusion, but there is nothing logically wrong with it, it's simply a matter of fact that one has to consider when one wants to construct sound arguments, so as to never equivocate any two different meanings of the same word. The binary determination is only possible either for cases which evaluate to the same truth value with every conceivable definition of a word, or once you pin down the exact meaning that is intended in a given context.
Part of the problem with your arguments indeed seems to be equivocation. There is a definition of slaves that hinges on complete unfreedom, which is roughly what most people think of if you don't specify any specific definition - let's name that a slave1 for the purposes of this discussion. Then, there are definitions based on certain philosophical arguments that try to show how, for example, socialism produces similar power structures to "traditional" slavery in certain regards, we'll call that a slave2. (Similar arguments exist for capitalism, and many other power structures.) Now, you come along and say "requiring doctors to provide a service is making them a slave2", which is actually a perfectly reasonable statement to make - except you obviously imply "which is the same as a slave1, and everyone knows that being a slave1 is bad, therefore, requiring doctors to provide a service is bad", and that's just an equivocation fallacy that you employ to avoid having to justify why one is as bad as the other, where that is not the slightest bit obvious if you look at the actual circumstances that slave1s lived in and that doctors live in nowadays.