You're missing the most important bit - the one this whole thread is about.
The 24 hour system: 23 -> 0 -> 1
The 12 hour system: 11 PM -> 12 AM -> 1 AM
In the 24 hour system, there's a single point where the new day starts, and it's the transition from 23 to 0.
In the 12 hour system, where does the new day start? Numbers tell you it's 12 -> 1, but it's actually 11 -> 12. You have no way to figure the answer to OP's question out without additional context.
As others already pointed out in this thread, a 12 hour system using 0 instead of 12 would make it much more intuitive, although now you'd end up with either using 0:00 PM for noon, which feels strange, or using 0:00 AM and 12:00 PM, which is inconsistent. The 24 hour system has no such issues and has a massive advantage over creating new systems - people are already familiar with it.