Let's say an ArmorStand has 2 tags, working & armorstand.
If we were to enter execute @e[type=ArmorStand,tag=working,tag=!armorstand] ~ ~ ~ say hi! it does not execute as expected, since our ArmorStand does have the armorstand tag.
But when we type in execute @e[type=ArmorStand,tag=!armorstand,tag=working] ~ ~ ~ say hi! it does execute, even though we still have the armostand tag.
It seems as though the order of which we enter the tags is dependent on whether or not it executes.