technically there’s no 12am or 12pm. it’s just 12 noon and 12 midnight. but for some situations it’s easier to have 2 labels than 4, especially when two of them are reserved to 1 min a day. so they just am and pm for convenience. so the logic you explain is used.
12:15 in the afternoon is uncontroversially 12:15 PM. I don’t think anyone could disagree with that. So are 12:10 PM, and 12:01 PM.
By extension, noon can only be 12PM, not AM, because the the moment we go from 11:59 to 12:00 is the very instant the afternoon starts.
(I use 24h clock myself but that’s another argument)
technically there’s no 12am or 12pm. it’s just 12 noon and 12 midnight. but for some situations it’s easier to have 2 labels than 4, especially when two of them are reserved to 1 min a day. so they just am and pm for convenience. so the logic you explain is used.