It is all to do with the emitted radiation and the half-life of the
source.
Carbon 14 is a beta emitter with a half-life of 5570 years.
1. Beta
particles have a short range in body tissue and so cannot penetrate far.
2. With a half-life
of 5570 years if any is injected into your body it will only have decreased in strength by just
over 1% during say 100 years of your life. Do you really want to walk around with an
increased radioactivity level for that long??
Of course a small fraction of the carbon
atoms in your body are carbon 14 so you are already radioactive!! Don't worry – the activity
level is very low.