Hanging up on listeners should be an option but an option of last resort. Some listeners do cross the line beyond all reason and decency. When I was first starting out in radio I was counseled to hang up on this type of listener rather than retaliate and making matters worse.
When your in this situation and you're dealing with an unhappy listener it is better to exercise patience,civility and understanding but when that listener makes it clear that there will be no civil dialogue(ie continued profanity,threats etc)it is sometimes better to end the conversation.
Do your best to address the listeners concerns and do attempt a civil dialogue but if it doesn't work it's better to terminate the conversation as opposed to getting your buttons pushed and doing something really stupid.