grammar - Subject versus object in a sentence: how are they determined?

For example, if I tell

“I'm write-only”

am I perceived as subject (who is writing) or as an object (who is written)?

Related question:

Answer

You should be careful to distinguish between syntactical labels and semantic labels. Subject and object are syntactic terms: they mostly say something about the form of the sentence, the way it is ordered. Agent and patient are semantic terms: they apply to meaning only.

(Note that the word "I" is one of the few words in English that can only be used as subject (or subject complement). You can't say "the dog beats I": if "I" is object, it should be "me".)

I beat the dog.

The agent of a sentence is the person or thing that acts upon some other thing. The patient is the person or thing that is acted upon. "I" is the person that acts, so that "I" is the agent. "The dog" is the patient.

The subject of the sentence can be found by answering the question: who is it that "beat"? - It is I who beat the dog. Therefore "I" is also the subject. You need to always take the full predicate, that is all the verbs in the clause, in your question to determine the subject.

The dog was beaten by me.

Who is the person that acts? - Me. Therefore "me" is the agent.
Who is it that "was beaten"? - The dog. Therefore "the dog" is the subject. As you see, in passive constructions the subject is usually the patient (or recipient: there are more than just two semantic roles).

[Edited:]
In your example "I am write only", the subject is "I", as Red showed. But I think you want to know whether "I" is the agent or patient of "write" in your sentence. That depends on the meaning of the sentence, which is not clear without context. Since "write-only" is mostly used with computer memory, I will assume that you mean "I" to be analogous to this memory. The sentence to be analysed would then be "this memory is write only".

We could then ask this question: "when someone writes data to a disk, who is it that acts, and who is it that is acted upon?". It is evident that "someone" is the agent, and "a disk" is the thing that is acted upon: therefore the disk is the patient. It follows that in "this memory is write only", the memory is the patient in the context of writing data; the adjective "write-only" must therefore accompany its patient. This means that "I" in your sentence is most probably patient.