Remove old bathroom faucet
I suspect that you need to:


remove all possible trim and rings from the top.
unscrew a hex set-screw from the underside (see blue arrow) that clamps the unit to the deck by pressing up against the "hold-down plate" (see yellow arrow).
once loose, the hold down plate will slide away from the faucet body, allowing the faucet body to drop out from the deck, striking you in the nose, eye, or lip/front tooth.