Because they have a large charge, alpha particles ionise other atoms strongly.Beta particles have a charge of minus 1, and a mass of about 1/2000th of a proton.This means that beta particles are the same as an electron. Gamma rays have a high penetrating power - it takes a thick sheet of metal such as lead, or concrete to reduce them significantly.
The argument may be compared to filling a barrel which has numerous small holes in its sides.We stick the garden hose in and turn it on full blast.The water coming out of the hose is analogous to the continuous production of carbon-14 atoms in the upper atmosphere."Everything which has come down to us from heathendom is wrapped in a thick fog; it belongs to a space of time we cannot measure.We know that it is older than Christendom, but whether by a couple of years or a couple of centuries, or even by more than a millenium, we can do no more than guess." [Rasmus Nyerup, (Danish antiquarian), 1802 (in Trigger, 19)].