It works because of the way the while loop works: The conditional in the while loop always gets evaluated first, before the content of the loop block. The <A> operator, when used in a while conditional, assigns the line gotten from file A to $_, starting with the 1st line.

The body of the loop, again uses the <A> operator, which gets the next line; you can access a line only once using the <> operator. I use it directly as the key to the %pairs hash, so the key is the 2nd line. It assigns the value of $_ (which was set in the while conditional) to this element of %pairs.

The loop evaluates the conditional again, gets the 3rd line, and assigns it to $_, and the body does the same all over again with the fourth line. So the even/odd mechanism is caused by the double use of <A>.

If I wanted to key on the odd lines, I'd've used $pairs{$_}=<A>;