shouldn't, couldn't

[joham]

---Do you know where David is? I couldn't find him anywhere.
---Well, he ______ have gone far--his coat is still here.
This was one of China's College Entrance Examination questions. The given answer was 'can't', but I wondered if we could also choose another answer: shouldn't.
Might I ask native English teachers to help me? Thank you very much.

 

[riverkid]

---Do you know where David is? I couldn't find him anywhere.
---Well, he ______ have gone far--his coat is still here.
This was one of China's College Entrance Examination questions. The given answer was 'can't', but I wondered if we could also choose another answer: shouldn't.
Might I ask native English teachers to help me? Thank you very much.

We don't normally use 'should' for pure speculation, Joham. Though 'should' occupies the same level of certainty range as 'probably/likely', it is used when we have some personal knowledge or greater in depth knowledge of a situation.

A: Where's your mom?

B: She should be at work.


Well, he probably/likely hasn't gone far--his coat is still here.

It's interesting to note that we have a purported present tense verb, 'can' being used [in the negative] to describe a past tense. The tenseless modal 'could' could/can also be used here.