Hexbear argument.

Assuming that you’re referring to “pulling information out of your ass”, you could try: “Pulling facts out of thin air” or “making it up on the go”. Getting more creative with it: “unscripted intellect”, “on the spot expertise”.

Malarkey Nonsense Fabrication

Wingging it.

A real gentleman would probably say “conjecture” or “unfounded information”, but a less explicit word is “nonsense”

Amateur hour

Made up on the spot.

Anyone who says asspull probably isn’t pulling any ass.

i’m just spitballing here… i’m thinking perhaps… maybe… does this resonate… have you considered… from another perspective… possibly… informed opinion… its likely… in the ballpark of… something like…

Rectally sourced figure

Somebody is trying to send a spicey work email lmao

Deus ex Machina?

deus ex machina

An “ad hoc solution”?

Pulled out of thin air

Cut from whole cloth

“A proctologist was needed to extract that information from its source.”

Goatse

An Araki

“He’s just pulling these figures out of his hat.”
“This step in the argument is a bit of a handwave.”
“I’m not sure we can afford to just guess here; let’s gather some real data.”
“Pay no attention to the man behind the curtain.” (PNAMBIC for short.)
“I’m concerned that the Emperor’s latest tailors may be in the pay of the Nudist Association.”

Alternative logic

Colonjecture.