Does objective thought cause authoritarianism?

This is an excellent and difficult question.

"An apple is an object but justice is a subject right?"

No. [In fact, when you observe an apple, you are the subject, so this question misuses the term "subject".]

Justice is an object, which can be identified and observed. But doing such requires more than just the senses. The difference between an apple and justice is that observing an apple requires only perception, whereas observing justice requires proper conception.

In the movie, Ayn Rand: A Sense of Life, Dr. Harry Binswanger says (and this is a quote from memory): "Ayn Rand understood the concept of 'justice' the way we understand the concept of 'chair'."

It is certainly true that it is harder to learn the correct meaning of the term "justice" than it is to learn the correct meaning of the term "apple" (or "chair"). But Ayn Rand held that such is possible. And from his quote, Harry Binswanger certainly believes that Ayn Rand had done the necessary mental work.

The difference between "apple" and "justice" as concepts, is that "justice" is more abstract. Abstract doesn't mean "fuzzy" or "subjective". It means that to form the concept of "justice" requires more thinking. And once the concept is properly formed, it's possible to recognize instances of justice and injustice with certainty.

Yes -- thinking, in the formation of, and in the application of a concept, is fallible. But such fallibility does not rationally call the meaning of all abstract concepts into question. In fact, "fallible" is an abstract concept which presumes the possibility of correctness.

An empiricist is a person who is skeptical about what human thinking is capable of. A classic empiricist argument is: "People disagree about abstract ideas, therefore abstract thought is unreliable. Sticking to concrete evidence is recommended." Your author above, Market Pennington, appears to be in this camp. Ayn Rand is not.

She held that thinking can and ought to be properly practiced, to form abstract concepts which are not only possible, but essential to human existence. To reject abstract concepts as such is to reject Man's essential tool of survival: his ability to think.

To claim that abstract terms are essentially subjective (and therefore of uncertain meaning) is to attempt to undercut any abstract thought. The belief that doing this will help combat authoritarianism is a fantasy.

When a Nazi or a Jihadist comes to town, "how can you be so sure?" will not be sufficient to combat their viewpoint. The proper method is to learn how to be sure that they are wrong -- that their views, and the implementation of their views, are unjust.

The imprint of Immanuel Kant can be seen throughout this question, i.e., the premise that reason (in a narrowly delimited form) is valid in the physical sciences but not in regard to values. In sharp contrast, Objectivism strives to show how reason is applicable to all of life's issues, including values and justice, and why value issues derive just as fully from reality as do issues in the physical sciences. When value-conclusions are tied to reality, the result is "authoritarian" only to the extent that one regards reality itself as "authoritarian." It is certainly true that reality itself does not allow man to do whatever he wishes with impunity, contrary to the deeply held wishes of so many opponents of reason in value issues, historically and to this day. If the constraining effects of "A is A" and the law of non-contradiction are "acceptable" in the physical sciences, why would they not also be "acceptable" in regard to values? Kant's answer (following the lead of religion) is that value issues go beyond the power of reason. Objectivism disputes that and vigorously shows man that the exact opposite is true and real -- and that man's only choice is to accept it or suffer the life-diminishing consequences that reality itself imposes. Reality is the "authority," not Objectivism. Objectivism is only the "messenger."