OBJECTIVITY
If by “subjective” we mean something like “first-person perspective”, that is a redundant concept since we are always in first-person perspective. A far more purposeful idea of “objective” and “subjective” would be as follows: given a first-person perspective, they would help identify what contents of our consciousness we can consider — within the context of our knowledge — as either “corresponding to reality” (i.e. “objective”) or “not corresponding to reality (at least not necessarily)” (i.e. “subjective”).
Hence, let me clarify what exactly does Objectivism mean by “objective”. “Objective” denotes a relationship between reality and consciousness wherein the facts of reality are grasped by the consciousness either by direct, i.e. irreducible awareness or by applying reason to direct awareness. The purpose of the concept of “objectivity” is to distinguish between (a) the contents of consciousness drawn directly from reality or by applying reason to such contents, and (b) the contents of consciousness that are results of non-rational faculties, such as emotion, intuition or imagination; (a) is objective while (b) is subjective. To be sure, yes, emotion, intuition and imagination can tell you about reality only if processed and validated by reason, but by themselves, they are non-rational, subjective, i.e. not necessarily corresponding to the facts of reality.
Hence, let us address the statement: “Consciousness is subjective”. Now, the fact of awareness is a self-evident fact. In other words, it is an objective fact about consciousness that consciousness exists. Now, awareness is always awareness of something, i.e. a fact of reality of some kind; it can be grasped through our senses or grasped through what we call “introspection” or “self-awareness”, but the fact is we are aware of something; something is there, even if we do not know what its nature is. A sensation, an emotion, a thought — all these are facts of some kind. For example, if we feel scared, there may objectively be no threat, but the fact is that we are scared; the fear present in us is an objective fact about our consciousness that we can be aware of directly. Taking a more extreme example, if someone has a hallucination of a monster, there may objectively be no monster, but the fact is that they are hallucinating; the hallucination in their minds is an objective fact about their consciousness, a fact that can be addressed objectively (e.g. through therapy or medication).
The contents of our consciousness may or may not correspond to facts by themselves, but they are themselves facts about our consciousness. It is with the help of such facts that we can identify certain states of mind that arise from certain conditions, such as joy or confidence. Once we identify these states, we can then apply our reason to identify their causes and see whether those causes are rooted in objective reality or not. If they are, then we call them “objective” as a shorthand for “based on what is objectively the case.” For example, my confidence in taking up a job may be based on real skills (objective cause) or delusions (subjective, irrational cause).