Accurate comparisons of risk in sport are hard to come by, because it’s hard to compare like with like (“climbing” could cover anything from bouldering to free-climbing the Salathé Wall, for instance); micromorts are a thought-provoking measure of risk.
Cycling is generally [citation needed] considered to be roughly as dangerous as walking, per mile; but the risk of death or serious injury is outweighed several times over [citation needed, but that’s what the UK health authorities say] by the health benefits of exercise. On average, it looks like you’ll live longer if you cycle.
Edited to add a nice link.