If you would like to explore whether the concept of a “subconscious” or "unconscious" is falsifiable, then do so (you will have to define “subconscious" and/or "unconscious" first).
You're missing the point. Suppose I wanted to defend the opposing viewpoint--that "unconscious mind" is falsifiable. What is my burden? To explain a process in a human mind that a human isn't aware of? Why couldn't the claim apply to dog minds or robot minds? "Unconscious" says nothing, so it makes no sense to me to say that "unconscious is falsifiable".
But I'll try to table that for now because we're just running in circles; apparently you're imagining that I'm acknowledging that "unconsciousness is not falsifiable" has a meaning and am disagreeing with it, despite my begging of you to supply a meaning.
You addressed the "cup falsifiability" issue by first converting the incomplete thought "cup" into a claim, such as "what I think is a cup is actually a cup". So since I have no idea what it means to say "unconsciousness is falsifiable" even hypothetically, let me follow this pattern. "What I think is an unconscious mind is really an unconscious mind".
The wiki definition of "unconscious mind" sounds good enough--a process of the mind that a person is not aware of. For something to be called "mind", we can focus on a particular area that interests me--intent. Intentional actions have certain properties that we can test; focusing on the example of drinking from a cup, if this action were intentional, it would involve: (1) Perception of a cup, (2) setting a goal involving the perceptual object--drinking from a cup (which itself involves such things as planning, which suggests perceiving or recalling potential uses of a cup and ways of using it), and (3) carrying out that goal.
Anything that is a goal-seeking behavior involving processing of perceptual capabilities is worthy of being called a process of the mind. Something that a person self-reports to not be aware of I can meaningfully call unconscious. Were I to find a class of apparent goal-seeking behavior that a person self-reports they aware of, I can apply a test to that class of behaviors to determine if it is indeed a goal-seeking behavior. For example, I can influence the perception of the involved object during the action (say, making a small movement of the cup), and observe if the resulting behaviors adjust accordingly such that the goal is still met (arm movement adjusts in such a way to compensate and still pick up the cup). If such behaviors do not adjust to meet the end goal, then I have a problem establishing that they are indeed intentional, because I have problems establishing that they are goal-based as I originally suspected.
That in mind, I have described a "cup" and a way of verifying that the "cup is really a cup", but my reservations here involve an entirely different kind of burden than falsifiability. The reservations involve whether or not the term "unconscious mind" plays a
useful role in the description. For example, this is simply one particular description... what other kinds of descriptions can be given using the term? Would I be better off simply calling this "unconscious intent"? Or even better off simply calling it intent that we happen not to be aware of?
(ETA: It's actually even slightly worse than this, because there may be a use for the term "unconscious mind"--a refinement of the concept--that makes sense, that still shouldn't apply in this scenario; for example, were I to actually find a partition of behaviors, where one would qualify as mind in a similar way that I qualified intentional behaviors above, but where a subject could not attend to; thus it's not so much like we're trying to falsify a theory as it is that we're trying to figure out if there exists a "fit" for the term "unconscious mind" into an existing system).