At school I was taught in metric. We measured in mm,cm and metres. But if something was 100mm we said 10cm. If it was 105mm we referred to is a 10 and a half cm.
So why has the cm fallen out of use?
Schools start by teaching using cm because at that age children are also learning the basics of counting and measuring 100mm is quite difficult if you are only confident using numbers up to (say) 20.
If you are measuring something arbitrary for learning purposes - like the span of your hand - then using whole numbers of cm is accurate enough. It then provides a route to teaching the concepts of fractions and estimating, so your measurement becomes (say) six and a half centimetres.
When you get more confident handling larger numbers, and the need for accuracy grows, it makes sense to switch to using mm as these provide for a good degree of accuracy for most purposes whilst not being difficult to use for larger measurements.
A good reason for
not using cm is the potential for confusion. For example, if weather presenters said 10cm of rain had fallen it would be quite possible and reasonable to mishear that as 10mm, the error isn't immediately obvious because a factor of 10 difference is within expectations. If everyone sticks to mm or metres then the difference factor is 1000 and an error
should be obvious just from the numbers. If we get 10 metres of rain we ought to be very worried.
Likewise, making it easy to spot (and avoid) errors is one of the reasons why cm are frowned on in engineering and construction. This is even more important where imperial measurements are still used or familiar. Going to a timber merchant and asking for 2m of 4 by 2 could lead to disappointment if what you really wanted was 40x20mm.