This is an example of hypercorrection, which is when native speakers make an accidental error in their zeal to avoid a different error.
In this case, the error that's being avoided is the error of writing "you and me" in subject position, as in the following sentence:
You and me are going to the store.
This is formally incorrect, although it's very common in contemporary spoken English. Because they have been taught that this is incorrect, many people hypercorrect and change "you and me" to "you and I" in all positions. That is, they incorrectly learn the rule about when to use "you and I", and so produce sentences like the following:
You and I are going to the store. [Correct]
He'll come to the store with you and I. [Incorrect]
I think your teacher is either "full of it" or "misinformed"
While it may be true that in English we usually enumerate parts of the body from the outside in, I'd suspect it has more to do with creating a physical starting point that is furthest from our eyes and looking for a way to create a list without forgetting something. I doubt this is limited to English, but is more of a "human" thing.
For random objects, I'd suspect people probably sort from easiest to recall to most difficult, or from most to least favorite, from biggest to smallest, by what sounds right or just randomly... or according to a set phrase, rhyme or song that's established culturally.
Lions and tigers and bears, oh my!
It's raining cats and dogs
strawberry rhubarb pie
They fight like cats and dogs
They're playing a game of cat and mouse
I'll have a ham and cheese sandwich
Would you like some cheese and crackers?
I'm having a wine and cheese party
I feel like a rum and coke
I'll take a Coke and Lime
In some of those examples, the more important element is stated first, but in many, the order has been established naturally, with less importance to order. Saying that, I'm sure there are certain patterns you could find based on how things sound together, or how many syllables there are... but the opposite is not wrong.
Best Answer
It is grammatically correct in this sentence, but there are conditions where it would be grammatically incorrect. The "more" in your example is modifying the verb "cover," whereas I believe you're reading it as modifying the adverb "later." "More" is clarifying the comparative degree of the verb (we will cover it in more detail than we just covered it now), while "later" is indicating when the action of covering the topic more will occur.
However, if the speaker meant to use "more" to modify "later," such a sentence would be gramatically incorrect.
As you can see, this would be grammatically redundant, as the word "later" already means "more late." So, to modify it with the word "more" is unnecessary.