Why does a comma go before the closing quotation mark?

Hi,

Why does a comma go before the second set of quotation marks?

For example:

"I'm sorry Gaz, but it's just not working out," said Mandy. "It's not you; it's me."

It seems arbitrary that a comma should be part of the direct speech. My character Mandy hasn't paused for breath! I'm sure there must be a grammatical reason for this convention. Does anybody know?

There are various style guides that discuss this kind of thing in detail.

Here is the way I think about it.

Mandy may not have paused for breath, but she would have slightly paused. I'd write the direct speech as "I'm sorry, Gaz, but it's just not working out. It's not you; it's me." The period represents a pause.

If you add said Mandy as in the sentence above, it looks odd to precede it by a period, so a comma is normally used instead.

Best wishes, Clive

Thank you.

So for the cases below, commas will be placed inside the quotation marks, no matter how short the content in quotes is.

Is this right? I found the following partical sentences from the Collins/Cobuild Compact English Learner's Dictionary, which I presume is published?? by a British  company, and thus follows the British convention.

According to AME, commas will go inside:

... must have a word such as 'a,' 'an,' 'the,' or 'my' in front of it.

... For example, you can say 'She was glad,' but you do not ...

But according to BrE, commas will go outside of the quotation marks. Right?? 

... must have a word such as 'a', 'an', 'the', or 'my' in front of it.

... For example, you can say 'She was glad', but you do not ...