There's quite a lot of language stuff you don't realise if you grew up with it. Sometimes you learn a rule without knowing what on earth the rule actually it. I had this come up once in a Danish class. The choice was between "hans" and "sin" which is a somewhat subtle thing. The thing is I never got any of the answers wrong, but I still don't really understand the difference.
On the learning side, you also often get told rules that don't entirely make sense. For instance I'm told in a Mandarin class that there's a difference between 不 and 没 which is whether it's subjective or objective that something isn't true. But that's neither clear when saying something, nor clear in terms of examples I've been given. What's really weird is I speak another Chinese dialect that also has this distinction, and I also can't tell you the rule there.
> I'm told in a Mandarin class that there's a difference between 不 and 没 which is whether it's subjective or objective that something isn't true.
I don't think that rule holds. 没 is usually used to negate either 有 "have" or something in the past. E.g. 我没告诉你。 "I didn't tell you." 不 is used for everything else, i.e. 我不告诉你。 "I'm not telling you." (The interesting thing is that "have" also has a past aspect in English, e.g. "I have told you." But Mandarin doesn't use 有 as a general past marker, only the negation 没)
> I speak another Chinese dialect that also has this distinction, and I also can't tell you the rule there.
Which one? Is the rule the same as in Mandarin, i.e. can you produce correct Mandarin sentences despite not knowing the rule, relying just on intuition? I think Cantonese uses 冇 to negate 有.
> 没 is usually used to negate either 有 "have" or something in the past.
More technically, 没 is the negative marker that applies to the verb 有, and 不 is the negative marker that applies to everything else. It isn't the 没 that marks a negative in the past as being past -- it is the (omitted) 有. That 有 is commonly not omitted in negative past sentences -- and it's also possible to use 有 to mark past time in positive-polarity sentences, though this is much rarer than the same marking in negative sentences.
There's a straightforward information-theoretic reason why 有 can be so commonly omitted -- it is the only thing that can ever follow 没, so actually realizing it doesn't add much. Everyone knows it's there.
Hm, I responded too quickly the first time. Some comments on the rest of your comment:
> E.g. 我没告诉你。 "I didn't tell you."
This is the same sentence as 我没有告诉你, also fully idiomatic. The past sense is coming from the 有.
> But Mandarin doesn't use 有 as a general past marker, only the negation 没
This is plainly incorrect. 有 is used as a general past marker. It just isn't obligatory in positive-polarity sentences. Here are some things Chinese people have said to me:
你在中国 有看见过 美国没有的水果吗？("Have you seen any fruits in China that America doesn't have?")
What I meant by "not a general past marker" is that you can't in general use positive 有 where you can use negative 没（有） to talk about the past. For example, you wouldn't say 我有看这本书。 to express you've read that book, but instead 我看了这本书。 Even in constructions like 有……过 the 有 is optional, so I'd say the past aspect is carried by 过.
On the other hand, maybe that is a shortening of an originally obligatory two-part expression similar to Jespersen's cycle, famously observed in the appearance of "pas" and ongoing disappearance of "ne" in French "ne ... pas". https://en.wikipedia.org/wiki/Jespersen%27s_Cycle
As you can see, there's more than one way to negate something. Well it's hard for me to know if the rule is the same, given that I don't really know what the rule is in either! As per my previous comment I can tell you what sounds right, but I can't tell you why.
The explanation for Cantonese in that Wikipedia article could be used just as well for Mandarin by simply replacing 唔→不, 冇→没, 唔好→不要, 咪→别,咗→了 ... so the rules are pretty much the same, they're just instantiated with different vocabulary.
On the learning side, you also often get told rules that don't entirely make sense. For instance I'm told in a Mandarin class that there's a difference between 不 and 没 which is whether it's subjective or objective that something isn't true. But that's neither clear when saying something, nor clear in terms of examples I've been given. What's really weird is I speak another Chinese dialect that also has this distinction, and I also can't tell you the rule there.