Is there a reason I can't take antioxidants while I'm getting radiation therapy?

Yes. Radiation takes advantage of free radicals formed in the field of radiation to cause dna damage targeted at cancer cells. Antioxidants are free radical scavengers, so they can potentially reduce the effectiveness of radiation treatments. It is best to avoid mega doses of antioxidants in the diet during and up to 6 weeks after radiation treatments.
Best not to take . Radiation works by creating free radicals. Antioxidants get rid of free radicals which has a protective effect that we want normally. But during radiation we create these in the area of the cancer to destroy cancer so we don't want to diminish this effect. All this is based on theory and radiation is so powerful that antioxidant are not likely to prevent this damage.