Why does cycling use a measure of time ("century") as a measure of distance? Wikipedia only attempts to explain the origin of the riding distance event but not why the term was used and why it "stuck".
A distance of 100 miles (161 km) is often referred to as a century. Century is also a common designation for 100 years, but that is not its exclusive meaning. The English word derives directly from Latin centuria, a group of 100 [etymonline]. This is a form of centum (or CENTVM if you will) which simply means (one)hundred.

A ride of 100 miles is thus aptly named a century ride, without having to resort to metaphors or figurative meaning.

Chris H mentioned another instance where century is used to count something other than years: In the sport of cricket, a century is a score of 100 or more runs in a single innings by a batsman [wikipedia].