Learn English – Phrase for “a strong reason for wanting something to happen …”

My first thoughts on reading the question were of the phrase 'I have a feeling of impending doom.' Since the word 'catastrophic' is used, this doesn't feel unduly strong.

Edit by Centaurus - I'm adding some lines from the reference the answerer has given in his comment below:

Many people experience strong feelings and sensations associated with fear and anxiety. They are especially powerful when they occur for seemingly no reason. Consequently, many people react to these "out of the blue" feelings with fear, which only serves to inflame them. To better understand these strong impending doom feelings, the anxiety symptom “fear of impending doom” is often described as one or many of the following:

• Feeling like something awful is about to occur
• A sense that something very dangerous is about to happen
• An overwhelming feeling you are about to die
• A strong feeling that something terrible is about to happen and there isn’t anything you can do about it
• A strong feeling of death and destruction that suddenly comes over you
• An overwhelming fear of impending doom, destruction, despair, and gloom
• A horrible feeling of doom and gloom that washes over you
• Fear of impending doom that begins or accompanies a panic attack or anxiety attack
• Such a strong feeling of impending doom that you feel you have to escape immediately or something terrible will happen

You want them to learn something the hard way.

It means to learn something by an unpleasant experience.