If you've ever had a place on your body that itched, you know that it annoys you until to pay attention to it (usually by scratching the itchy area). So if you're "itching to know" something, it means that the ignorance of this particular fact is going to annoy you until you find the answer.
To go from one extreme to another means, for example, to go from crying one's eyes out to laughing hysterically. Or from starving to eating so much that you feel like you're going to explode. Or experiencing such hot, dry weather for months on end that all the crops are dying to a sudden, torrential rain that lasts for days and threatens to flood the area. "One extreme to another" refers to polar opposites.
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