Is "The Dad is fishing" acceptable?

Solution 1:

Yes it is fine, it just sounds odd because it is very short and isolated.

Imagine if the student had made it a longer sentence about a whole family day out, it would sound fine.

The dad is fishing, the mum is sleeping in the long grass and their kids are playing a ball game.

I agree it does sound odd as presented, and it took me a few moments to realise it was a correct sentence.

Solution 2:

As an answer to the question "What's happening in this picture?" the sentence is fine.

You've said that he picture shows a father and son fishing, so all we know about the man is that he is the father of a son and he's fishing. Without a name for either person, the speaker uses the man's relationship as a sort of occupational title, calling him "the dad". This is similar to how we might refer to "the teacher" or "the doctor". It's fine to use any of these as the subject of a sentence. Note that it would also be grammatical and somewhat logical (but less likely) to say

The fisherman is hanging out with his son.

If the speaker were discussing their own father, we would expect not to see a definite article: it should be "my dad" or just "Dad" (capitalized because here it's being used more as a name than a description). And when discussing a known person's father we'd expect a possessive pronoun or the possessive form of the person's name: "his dad" or "Jordan's dad". Those situations are a lot more common than this kind of condition where the speaker needs to comment based on such limited information, which might be why the sentence sounds odd to you.

The only other thing that stands out about "the dad" as a subject is that it's somewhat informal. In a more formal setting we would usually use "the father" in place of "the dad". This comes up in, for example, news and legal reports, as in "The father of DJ Jeffries . . . isn't pleased with Kentucky" or "the trial court clearly . . . failed to accord the father the constitutional protections he was due". But in casual conversation it's fine to use "dad". I don't know whether formal language was important in this test, but if so "the dad" might have been too casual.