How does negation affect the use and understanding of “or” and “and”
If I want to negate a sentence such as
I like beer and whiskey. [Most commonly understood as, I think, I like beer and I like whiskey.]
I have to convert the and to an or:
I don't like beer or whiskey.
There's no sense of an or in the second sentence, so its inclusion seems a bit perverse. I realise that I could say
I don't like beer and whiskey.
but that would mean something different:
I don't like (beer and whiskey).
rather than the intended
(I don't like beer) and (I don't like whiskey).
So my question is: what's going on here? Why do we have to make this change?