Why can't humans avoid or resist radiation?

because background radiation is natural in the environment and everybody intakes a certain dosage of it everyday, so we are all slightly radioactive.

examples are Radon gas, food, some rocks (especially granite)

but on some occasions we do take in man-made radiation, such as nuclear.

there have been times in nuclear disaster like the Chernobyl incident, that the radiation had harmed living cells and caused mutation in DNA.

how much radiation of any form you take in depends on where you live and your activities (such as your job because some people like nuclear workers or x-ray doctors can be more exposed).

usually the percentage of background radiation is quite small, and alpha, beta and gamma rays can be deflected.

radiation poses a threat to humans because it mutates DNA, rewriting the genetic code that can lead to cancerous growth of cells. 5 or 6 Sieverts over the course of a few minutes will shred up to many cells for our bodies to fix at once. supposedly workers in Japan absorbed up to 1 Sievert of radiation while contending with a nuclear disaster last march. But their lifetime cancer rate was much higher, so I guess it comes with a cost.