He couldn't be a doctor. Those are crime syndicate tats.

Paraphrase: I don't suppose he's a doctor.

He can't be a doctor.

Paraphrase: No way he's a doctor.

can't is definite and certain; couldn't can be tinged with uncertainty.

But with the proper intonation, can't can express incredulity not certainty:

You're pulling my leg! Him, a doctor? He can't be a doctor. He's only 17.

He couldn't be a doctor. Those are crime syndicate tats.

Paraphrase: I don't suppose he's a doctor. Would a doctor have crime syndicate tattoos?

He can't be a doctor.

Paraphrase: No way he's a doctor.

can't is definite and certain; couldn't can be tinged with uncertainty.

But with the proper intonation, can't can express incredulity not certainty:

You're pulling my leg! Him, a doctor? He can't be a doctor. He's only 17.

He couldn't be a doctor.

Paraphrase: I don't suppose he's a doctor.

He can't be a doctor.

Paraphrase: No way he's a doctor.

can't is definite; couldn't can be tinged with uncertainty.

He couldn't be a doctor. Those are crime syndicate tats.

Paraphrase: I don't suppose he's a doctor.

He can't be a doctor.

Paraphrase: No way he's a doctor.

can't is definite and certain; couldn't can be tinged with uncertainty.

But with the proper intonation, can't can express incredulity not certainty:

You're pulling my leg! Him, a doctor? He can't be a doctor. He's only 17.