Somewhere along the way, the concept of counting what time of day it is - on a 12h scale - went wrong.
The 24h scale is also equally wrong but less so.
Starting at midnight:
Midnight (the word) makes sense, but why is it 12:00. I would propose it being changed to 6:00. Since (at least around winter time) its been dark for about 6 hours... This is not a very convincing reason ... yet.
Next take a look at 6:30 AM.
Most people are waking up for work or for grade school around this time. Since it is the time that 90% of mainstream society accepts that the day is beginning, 6:30 AM should be 00:30. (6 should be 0).
Noon will no longer be 12:00 it will now be 6 since it is halfway through the day.
When it gets dark, it will no longer be some time around 5:45/6:00 PM = we can now call it 12:00.
Of course nobody will ever succeed in changing the format of which clock system billions of people use, but I can always hope.