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.
It’s like that with every competitive game.
You see other people playing it and think “wow, that’s cool. I wanna try it”, only to be welcomed by what you just described. Your success then depends on whether you have a hard skin to endure the bullshit, or if you’re social enough to have others play with you that won’t dismiss everything you do so easily. More often than not we don’t have the patience/ability for either.