Why does sizeof(x++) not increment x?

From the C99 Standard (the emphasis is mine)

6.5.3.4/2

The sizeof operator yields the size (in bytes) of its operand, which may be an expression or the parenthesized name of a type. The size is determined from the type of the operand. The result is an integer. If the type of the operand is a variable length array type, the operand is evaluated; otherwise, the operand is not evaluated and the result is an integer constant.

sizeof is a compile-time operator, so at the time of compilation sizeof and its operand get replaced by the result value. The operand is not evaluated (except when it is a variable length array) at all; only the type of the result matters.

short func(short x) {  // this function never gets called !!
   printf("%d", x);    // this print never happens
   return x;
}

int main() {
   printf("%d", sizeof(func(3))); // all that matters to sizeof is the 
                                  // return type of the function.
   return 0;
}

Output:

2

as short occupies 2 bytes on my machine.

Changing the return type of the function to double:

double func(short x) {
// rest all same

will give 8 as output.

sizeof(foo) tries really hard to discover the size of an expression at compile time:

6.5.3.4:

The sizeof operator yields the size (in bytes) of its operand, which may be an expression or the parenthesized name of a type. The size is determined from the type of the operand. The result is an integer. If the type of the operand is a variable length array type, the operand is evaluated; otherwise, the operand is not evaluated and the result is an integer constant.

In short: variable length arrays, run at runtime. (Note: Variable Length Arrays are a specific feature -- not arrays allocated with malloc(3).) Otherwise, only the type of the expression is computed, and that at compile time.