True. I wonder whether a better translation of /Si ayah/ would be a colloquial/idiomatic phrase which is sometimes used to mean "father" but also sometimes indicates less respect, like "old man." However, "old man" has the limitation of needing to be paired with a personal adjective preceding the phrase, else it could mean any generic, literal old man and not someone's father. For example, "My old man doesn't work" or "His old man doesn't work." I suppose "The old man doesn't work" could also be a reference to one's father, but without surrounding dialogue or other contextual clues, it wouldn't be very obvious.
I know Duolingo is translating si straight as "the" in these exercises, and Duo favors lexical word-for-word translations over freeform ones.
But my understanding is that si is used to convey familiarity (through affection or disrespect, depending on the context), and "the father" sounds very formal and distant.
Wouldn't omitting "the" went just going with "Dad" (or maybe "Father" if you're kind of posh) be more in line with the actual meaning expressed in this case?
You should definitely get a local speaker to check my assumption on this, but what I suspect is that /Si/ is being used intentionally as a familiarity classifier. It's a marker that the speaker doesn't think very highly of the father. So, it's a way of implying "that loser" or (maybe sympathetic?) "the poor, dear man" does not work.
Sometimes, lexical word-for-word translation causes a person to totally miss the meaning and/or construct sentences which are unnatural patterns of usage or syntax, so adequate translation requires more than simple word-swapping.