Difference between "I don't believe it." and "I can't believe it."

Question

What is the difference between I don't believe it. and I can't believe it.?

For example,

A: I've heard John got that job.

B:"I don't believe it." or "I can't believe it."

Answer 1

Although there seems to be a difference, in fact, most times the two expressions are interchangeable in use. Or so say most natives in the language forums. Here is an interesting post:

There is very little difference between the two statements. To hair split, one can say 'I don't believe this' is an absolute rejection while 'I can't believe this' is less absolute and has a connotation of disbelief in something one has read or seen.
NB The intonation and stress when spoken is important and gives a guide to what the speaker means.

I think the NB is spot on. You can use both expressions in a situation, but it is the intonation that will give it meaning and nuance. You can trust Victor Meldrew from One Foot in the Grave! _{See video with plenty of intonations in the link! And try not to laugh!}

I don't believe it is defined as

An expression of surprise or incredulity, possibly bordering on vexation.

• I don't believe it—I have the winning lottery ticket!
• So you came crawling back to us after all. I don't believe it. (FreeDict)

The same dictionary says about I can't believe it/that/this

This information is so shocking or implausible as to be unbelievable.

• A: "Did you hear that Amanda got the promotion?"
  B: "Yep, and I can't believe it. I know I'm more qualified for it than she is!"
• Are they really closing McCauley's after 40 years? I can't believe it! (FreeDict)

I think trying to differentiate the two phrases by focusing on the difference between don't and can't won't get us too far.

Macmillan goes as far to conisder them as two versions of the same phrase:

can’t/don’t believe it

• used for emphasizing that you are extremely surprised or shocked
  used when something annoys you

You will find this Ngram interesting: On both sides of the ocean, I don't believe it is far more common.

PS: As a matter of fact, I think that gestures and mimics are just as important as intonation in what one means by this expression!