Useless, useless... logic is not English; the student wants to know when to use which form.
"My mother can speak Malay and English" would be a good answer to the question, "What languages does your mother speak?" "My mother can speak Malay or English" would be a good answer to the question, "The visitors can speak French, Malay, Chinese, and English. Will your mother be able to speak to them?"
"She is not good at writing and reading" should be "She is not good at reading and writing" in English (reading and writing is in the order we say it in English). In this particular case, "She is not good at reading or writing" would be equivalent, and you could use either one.
Sorry to be contrary, but you aren't differing. Charlie didn't say either usage was uncommon, merely that one of them was more common. And he's right.
Charlie has said that one form was more common than the other and my point is that this is not the problem of common usage. They are not these forms of an object therefore they cannot be compared.
I have said that this is the problem (or question) of logic, it did not depend on the language we used to write those sentences. To be more clear: these sentences that the poster has asked are not the same.