Since two triggers are trying to go on the stack at the same time, first your triggers are put on the stack since you are the Active Player (AP), then your opponent's triggers are placed on the stack on top since they are the Non-Active Player (NAP)
Instead, it is, as its name loudly suggests, a Dragon
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All that to say Cogsworth isnt invulnerable, but hes definitely a challenge to banish for your opponent, and makes your board a lot safer just having him around
I love coming here to see the clean art every month I was wondering tho, the Lugia and Ho-Oh immersives from last pack, does a full art of them each solo in a normal card aspect ratio exist anymore
And thats probably my own bias speaking