Adila, from her perspective in the depths of the curse, understands intellectually that there are people out there with different priorities than [i]stick[/i]. She understands that people have motivations like pride or jealousy or competition or protectiveness or love - she is aware that she has all of those herself, even. But none of them have the same utter immediacy of stick. The world orbits around it, her limited doggy mind processing all of the importance of saving Hyperborea, defeating Eupheria, all of her hopes and dreams - all that immense complication is condensed down into a single laser point that can only be articulated as get stick. Maybe bury it later. But get stick.

So even though Eupheria loves and cares for the Caduceus it isn't literally her entire world like it is for Adila - Caddy helps her get other things she wants. But for Adila, she has to win, and winning means getting the stick. She'd do anything for it - even being a bad dog and leaping up to grab it when Eupheria is distracted, grabbing it out of her hands, and bolting. It's not good but - but Eupheria hasn't thrown the stick [i]once[/i] and that makes it her fault too.