Why are grammatical subjects called subjects?

In a monarchical state a subject is "one that is placed under authority or control" (Merriam). If A is subject to B, A is figuratively beneath B. This meaning makes sense with the word's roots of under and throw (again, Merriam; quotation below*).

In grammar, though, the subject, as we all know, acts. (Yes, the grammar structure can be passive so that semantically the subject is not active; even still the subject performs the verb, which in a passive structure, is to receive the action.) It has agency. It is the noun (or noun phrase) doing the throwing under and doing the subjecting, not being thrown under or being subjected.

How did subject develop such seemingly opposed meanings? It can certainly make reading lit theory confusing.

*Middle English suget, subget, from Anglo-French, from Latin subjectus one under authority & subjectum subject of a proposition, from masculine & neuter respectively of subjectus, past participle of subicere to subject, literally, to throw under, from sub- + jacere to throw

Subject: the person or thing that performs the action or incorporates the action expressed by the verb, or is in the condition indicated by the verb. While it seems the subject initiates the action (especially with transitive verbs) the verb requires a "subject" to carry out or perform the action, hence the "subject" is submitting to the "verb" or let's say, "predicate".

The idea of the term subject in grammar is that which is placed under something. Object means that which is placed on top of something. If you see the verb of a sentence as the central word the subject is placed under the verb and the object is placed on top of the verb.

So you get a model of the sentence structure where the sentence parts are arranged like bricks in form of a tower and not as we are used to see sentence parts. We would arrange the sentence parts in a line from left to right.

The Latin terms were probably influenced by views of Greek grammarians. Personally I don't find the tower model bad. Another question: What optimal terms could one invent for subject and object? I think the best and simplest terms would be: Subject is the who/what indication of the verb (nominative) and object the whom/what indication (accusative). Unfortunately the terms nominative and accusative are no longer very helpful in English because the two cases have the same form (with the exception of some pronouns). In English these two cases are distinguished by position, before or after the verb in normal sentences of statement.