"Subjective" means "related to the subject". E.g. "subjective thinking" means thinking that would reach a different result with a different subject.
Note: The subject means the person or thing that does the action. The object means the person or thing that receives the action. Subject is actor, object is acted on. Those terms are used in grammar a lot. I wrote this post because I thought applying the grammar ideas to the subjectivity issue is clarifying.
Joe reaches one conclusion, e.g. "I like steak." while Sue reaches another, e.g. "Steak is OK but I prefer shrimp.". The subject in both sentences is "I", but the first time that means Joe and the second time Sue. So the subject changed and the preferred food changed. Preferred food depends on subject.
Objective thinking means thinking that depends on the object. If "steak" is the object of the verb "like", then objective thinking would try to give an answer without even knowing what the subject is. It doesn't matter who is doing the liking (the subject), what matters is what is being liked (the object).
Those are just historical roots. Today, subjective means: arbitrary, whim-worshipping, refusing to deal with reality, illogical, and more. It's associated with people claiming stuff is a matter of personal taste in order to ignore criticism. "You can't judge me negatively, I'm the subject and you don't know enough about me. You only know about the object but not the subject, so shut up. Everyone can live in their own world where they are the subject and they can do no wrong."
Meanwhile, objective has come to mean unbiased thinking that looks at the whole picture and does rational analysis. Instead of pretending you can reach any bullshit conclusion just because you're the subject, objective thinkers try to understand the facts about the object in reality so they can reach a true conclusion. Truth is objective, not subjective. What's true doesn't depend on who is speaking.
Grammatically, you can also talk about verbs with an object but no subject, e.g. "Eating steak is fun." There, the verb "eating" has no subject and is just talking about the general concept of any subject doing eating, rather than connecting the statement to a particular subject. (The grammatical subject of that sentence is "eating steak" itself, which is the subject of the verb "is" and which is.) That's an impersonal statement because it lacks a human subject. That means only objective analysis makes sense.
Yet, for some issues, what is true does depend on who is speaking. E.g. "I like steak." is true for some subjects and not others. Some people like steak and others don't.
This is an aspect of a broader issue: truth is contextual. A statement like "The box on the left is brown." Is that true? Well it depends what box is on the left. That box is the grammatical subject of the sentence, but it's not a person with "subjective" tastes or personal preferences. The situation: time, location, stuff at that location, etc. is the context.
People's tastes are context too. Joe liking steak is context just the same as what boxes are in the room is context.
If people would say "Truth is contextual.", it wouldn't cause problems. "Contextual" doesn't have all the anti-reality and anti-reason associations that the word "subjective" does.
Also, subjects exist in objective reality. Joe exists in the objective world, along with his preference for steak. Just like the box on the left exists in the objective world and has a color. And no one is confused with the box, they get that whether the left box is brown depends on what boxes are present and what their colors are and those are all factual matters about the real world.
It's mostly just when the subject is a human being that people start claiming stuff is "subjective". They know their personal feelings have no control over the reality of boxes and colors, but they believe their personal feelings can mean "What's right for me isn't right for you and no one is wrong." Which is true to some limited extent, e.g. Joe can be a physicist and Sue a chemist and neither person is wrong. But that's not because choice of career is an arbitrary choice. People often pick the wrong career and end up unhappy and unsuccessful. It's just that context matters. If Joe has skills and interests related to physics, then a physics career can fit him well. If Sue is in a totally different situation (context), then a different career may fit her. The actual facts of Sue's situation are relevant for Sue's career and can be evaluated in an unbiased way. Talking about Sue is like talking about the objects in one room, and talking about Joe is like talking about the objects in a different room, so it's no surprise that in one case there could be a brown box on the left and in another case there isn't. None of that is "subjective" in the way people mean it today, although it is "subjective" in the sense of dependent on the subject (actor) or, more broadly, dependent on the context.
An objective test?