Q:

The usage of either or

Here are a few sentences. The first one made me confused.

You can have either the £15 cotton top or the £17 cotton-and-polyester blouse. You can't have both. 
Which of these apples would you prefer? ~ I don't want either of them, thanks.
The sisters in the photograph were standing on either side of their dad. (OR: ...on each side..., OR: ...on both sides....) 

I can understand 2nd and 3rd sentences, but the first sentence sounds more like "you can have both of them" in terms of meaning. And I can't find a general rule or formula if somebody asks me when "either" means both and when it means none of them. But when I ponder it a little further I thought maybe if I can rewrite the sentence by omitting "or"  as 

You can have either the £15 cotton top and the £17 cotton-and-polyester blouse.  

This time could it mean "you can have both"?

A:

"Either" here is being used as an exclusive-or, which means "one but not both". Technically, saying "You can't have both" is unnecessary, as that's what "either" means.
So therefore, you cannot say "either this and that" - "either" and "and" just don't work together, logically.

