How can a 14 year old teen develope throat cancer?

It's rare. Throat cancer is very rare in teenagers. The most common age of throat cancer patients is 50-70 years. However, certain risk factors, such as smoking, alcohol use, gastroesophageal reflux, and exposure to chemicals, can promote earlier development.
Rare but it happens. Smoking, dipping, chewing tobacco. Airway papillomas, certain genetic dispositions, previous radiation therapy, and plain bad luck can cause throat cancer in a teenager. It does happen.
Genetics. Pediatric patients with squamous cell carcinoma of the larynx may have had radiation to the neck for another reason, or be part of an inherited risk group. Here is an abstract citation if you are interested: mod pathol 1999;12:130a(760).