"The rest of the world, no matter their number, has no right to dictate that he shares his knowledge"
Perhaps not, but why should I be allowed to dictate to you what you are allowed to do with knowledge that I impart to you? Put another way, if I publish a paper describing knowledge I have developed, why shouldn't anyone who receives that paper be permitted to spread that knowledge further -- and if so, why not by simply giving copies of the paper to others?
"Anything less than that is slavery."
I think perhaps you missed part of the definition of slavery:
https://en.wikipedia.org/wiki/Slavery
Did anyone say that anything about forcing someone to work? Did anyone say anything about not paying someone for their work, if that person demands payment? No, nobody is talking about that. What we are talking about is what we can do with the products of a person's work once those products have been made available to us.
Almost all the scientific papers that are published today are written by people who are paid to do research and to share the results of their research with others. Very few scientific articles are written by unpaid volunteers (even grad students typically receive some compensation for their time). This is not a question of paying for research, because research is already paid for and would continue to be paid for in the absence of the publishing industry. If a researcher does not want other people to read the articles he writes, he can refuse to publish -- he can take his secrets to his grave.
Copyrights are not and have never been a natural right. Copyright, as applied to academic publishing, has only ever been a system for promoting the dissemination of knowledge by monetizing a publishing industry. Researchers routinely assign their copyrights to publishers when they publish articles, losing whatever claim they had to preventing copies of the work from being made. We no longer need publishers to spread knowledge across our nation because we have a better system, the Internet, and therefore copyrights on academic work have outlived their usefulness.
The comparison to slavery is pedantic and misleading. Slaves do not have a legal option to not do as commanded by their masters; in a world without copyrights on academic work, researchers would have a legal option, which is not publishing their work.
"In the same way, one man does not owe another man money, a job, a scientific article, or a movie just because he happens to be able"
Which is fine: you are free to not publish your work. You will probably not get very far as a career researcher if you refuse to publish, but that is your problem and not mine. It is not really society's problem either, because there is no shortage of researchers who willingly publish their work, nor is there any shortage of researchers who will willingly publish their work in the absence of copyrights. Ayn Rand's notion that copyrights are a necessary function of government was absurdly misguided, but we can forgive her because as an author she profited from copyright (unlike researchers, who rarely profit from copyrights on their knowledge). Copyrights are a means to an end, and in the age of the Internet, copyrights on academic works have completely outlived their usefulness.
Your right to not teach others what you know is not in question here; rather, the question is whether or not I can teach others something you taught me. Considering that human civilization exists because we have spent generations passing knowledge along and it was only very recently that we even considered forbidding people from spreading knowledge, I would think that there is no real moral dilemma there and that the answer to the question should be obvious.