husten
to cough
To expel air from the lungs suddenly and noisily, often as a symptom of a cold or irritation of the airways.
Wegen seiner Erkältung musste er die ganze Nacht husten.
Because of his cold, he had to cough all night.

to cough
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to cough
To expel air from the lungs suddenly and noisily, often as a symptom of a cold or irritation of the airways.
Wegen seiner Erkältung musste er die ganze Nacht husten.
Because of his cold, he had to cough all night.

You can recognize the colloquial meaning by its fixed structure: there is always a person in the dative to whom one "etwas" or "was" hustet. If this structure is missing, the literal meaning is almost always intended.
Er hustet stark wegen seiner Allergie.
He is coughing badly because of his allergy.
In its main meaning, 'husten' (to cough) is used as an intransitive verb, usually without an object. The sentence 'Das Kind hustet' (The child is coughing) is already complete and grammatically correct.
Wenn man krank ist, sollte man in die Armbeuge husten.
When you're sick, you should cough into the crook of your arm.
The idiom 'jemandem etwas husten' has a fixed structure. The person refusing is the subject. The person whose wish is being rejected is in the dative.
Mein Chef will, dass ich am Wochenende arbeite. Dem werde ich was husten!
My boss wants me to work on the weekend. No way!
This idiom is very colloquial and expresses a defiant refusal. You should only use it in very informal situations.
Du glaubst, ich helfe dir nach dieser Lüge? Da kann ich dir was husten!
You think I'll help you after that lie? No way!
to reject
'ablehnen' and 'jemandem etwas husten' can both express that you do not want to do or accept something. 'ablehnen' is neutral and fits many situations, for example with offers, requests, or suggestions. 'Jemandem etwas husten' is a colloquial idiom and sounds much stronger. You use it when you want to say very clearly: I absolutely will not do that. In normal or formal conversations, 'ablehnen' is more natural; the idiom fits more in casual, sometimes annoyed language.

Seinen Bericht soll ich auch noch schreiben? Dem huste ich was!
I'm supposed to write his report too? No way am I doing that for him!
Nach der Arbeit haben wir das Angebot für das teure Menü abgelehnt.
After work, we turned down the offer of the expensive set menu.