1

This won't happen again. I promise.

Vs

It can't happen.

What does the change of the auxiliary verb mean?

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Won't implies either a pledge, as in your example (I promise), or a confident prediction, or a refusal:

Abduction by Martians has dropped off since the 70s. I'm pretty sure it won't happen to you again.
No matter how much you offer I won't sell you my daughter.

Can't implies either an impossibility or a directive:

I'm sorry Bobby made that rude gesture. It can't happen again, because we've cut off his hands.
Yesterday Cathy sold one customer another customer's umbrella. This can't happen again.

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  • can't happen means "this mustn't happen again?"
    – user2492
    Apr 23, 2014 at 14:04
  • @username901345 In the umbrella example, yes.
    – StoneyB on hiatus
    Apr 23, 2014 at 14:04
  • so it doesn't mean the impossibility of the event occurring again in the future.?
    – user2492
    Apr 24, 2014 at 3:14
  • @username901345 Not in that case, no.
    – StoneyB on hiatus
    Apr 24, 2014 at 9:23
  • 1
    @username901345 The reference in this case is to the future, but it does not say that it is impossible that the event should happen in the future: it says that the event must not be permitted to happen in the future.
    – StoneyB on hiatus
    Apr 24, 2014 at 10:00
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Won't implies that you are personally involved in preventing it recurring.

It won't happen again, I'll personally make sure it doesn't.

Can't implies that someone else, or something else, is responsible for preventing it recurring.

It can't happen again. They've changed their procedures.

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