Since it's a cat, I feel like it may be in reference to this book titled 吾輩は猫である.
ワガハイ or 吾輩 in kanji, is an archaic first person address term.
Why does it use that? and what does it really mean?
It carries a feeling of pompousness and self-importance (which is of course very important for a cat). Wikipedia says:
Sōseki's original title, Wagahai wa Neko de Aru, uses very high-register phrasing more appropriate to a nobleman, conveying a grandiloquence and self-importance intended to sound ironic, since the speaker, an anthropomorphised domestic cat, is a house cat, not feral.