[wongarsu]

>You basically pretend that there is no problem and that time is perfectly accurate, up until you have a minute with 59 or 61 seconds.

Time is perfectly accurate, including all the minutes with 59 or 61 seconds. UTC is perfectly defined as atomic time (TAI) with an offset to keep it within 0.9 seconds of UT1 (time as measured by the rotation of the earth). Every time we increment or decrement this offset, this leads to leap seconds. But since 23:59:60 is a valid time (and distinct from 00:00:00 on days with leap seconds), there is no ambiguity here.

The problem here is how most computers handle this: introducing ambiguity by setting the clock backwards or forwards one second, instead of accounting for the fact that not all minutes have 60 seconds. Google did a pragmatic fix for their use case by squeezing leap seconds into the surrounding seconds, stretching them. It works for them, but now their "seconds" are not actual seconds anymore.