Subjective means according to opinion. Objective refers to facts. Then there are the subject and object of a sentence. You can object to something you've been subjected to. And if you know a little bit of Latin, it seems weird that subject seems to mean throw under. What is the subject of a sentence being thrown under, exactly?
According to Online Etymology Dictionary, subject matter came from subjecta materia, meaning that which lies beneath. If you are studying a subject, you are hoping to discover something below the surface. Perhaps the sense of subject meaning recipient of action comes from the action of studying. By the 1630s, the grammatical meaning of subject had emerged. You can think of the subject as the topic the sentence covers, in a way.
A predicate, from the Latin praedicatum, is something declared. A sentence has a subject, which is the most important thing in the sentence but still below (subject to) the sentence itself, and a predicate, which is a declaration about the subject. In the sentence Mushrooms are beautiful but can be deadly, the word mushrooms is the subject and the rest of the sentence is the predicate.
The predicate has a verb and sometimes one or more objects. You can already see the -ject (throw) that object shares with subject, this time paired with ob- (against). When you object to something, you are throwing something in front of or against it. In the 15th century, object in the sense of purpose or aim came from the Latin obiectus, meaning that which presents itself to the sight. The object of a sentence is the goal toward which the subject strives.
Isn't the object the recipient of action?