It's cause PHP associates the if-then-else pair only with its immediate "else" option, not with the entirety of the line.

Let's go by parts.

$a == 1 ? "one" : $a == 2 ? "two" : $a == 3 ? "three" : "other"

Is $a equal to 1? If so, we're "set" to the value on the left, which is "one", if not then we're set to the value on the right, which is $a == 2. $a is not equal to 1, so we're set to the right value, $a == 2.

This replaces the relevant part, $a == 1 ? "one" : $a == 2, with $a == 2. So we're left with:

$a == 2 ? "two" : $a == 3 ? "three" : "other"

Next, is $a equal to 2? If so, we're set to "two", if not we're set to $a == 3. The comparison is true, so we're set to the value on the left, "two". The relevant part here is $a == 2 ? "two" : $a == 3 only, so it replaces it with "two" cause again, PHP is only associating with its immediate pair. So now we're left with:

"two" ? "three" : "other"

Finally, is "two" truthy? If so, we're set to "three", if not we're set to "other". Since "two" is truthy we're then left with "three".

It's super confusing for sure.