Why don't we use xor (or nand)?

Solution 1:

The xor of two statements is the equivalence of one of them to the negation of the other. More generally, the xor of $n$ statements is defined as the assertion that the number of them that are true is odd. This is especially inconvenient in stating either the antecedents or consequents of theorems, which are naturally stated as material conditionals and hence as inclusive disjunctions. And we frequently wish to state some $n$ statements are all equivalent. Further, the inclusive disjunction of $n$ statements - i.e. the claim that at least one of them is true - is also frequently useful, e.g. because some claim of interest follows from any one of them.