Radiation to the jaw due to head/neck cancer can cause problems with dry mouth as well as an increase of risk of infection of the jaw. Generally radiation of the upper jaw area results in dry mouth due to damage of the parotid (salivary) gland. This makes you more prone to cavities. Radiation of the lower jaw area generally doesn't have a big an issue with dry mouth but since the blood flow of the lower jaw is poorer, theres a tendency for the blood vessels to die and this results in poor blood flow. This poor blood flow makes you more prone to infections after extractions. The consequences of a jaw infection are very serious and can result in loss of the lower jaw. I can understand why your dentist is very wary of removing the teeth.
You may want to post this question in the oral and maxillofacial surgery section and discuss this with an oral surgeon. They are more likely to deal with these types of situations and fits more into their speciality.