Why is duration quoted in years if it measures bond price sensitivity?

Duration started as a timing measure. Macaulay duration is the present-value-weighted average time to receive a bond's promised cash flows, so years are natural. Modified duration is derived from that timing measure and is used as a sensitivity multiplier for a small yield change.

That is why the same number can feel like both time and risk. If modified duration is 6.0 and yield rises by 0.25%, the approximate price change is -6.0 x 0.0025 = -1.50%. The duration number is quoted like a time measure, but when multiplied by a decimal yield change, it estimates the percentage price response.