The Speaker has to come from the House

The Constitution does not, it’s true, explicitly say the Speaker has to be a member of Congress.

Matthew Franck addressed this question in NRO the last time McCarthy was having trouble getting to the Speakership, in 2015, arguing that the Constitution implies that a Speaker has to be a member of the House.

Among his points: Accepting a non-member as Speaker would open the door to letting a Cabinet member be Speaker, contrary to the aim of the Constitution’s incompatibility clause. I’d add that you would also then have the possibility of a Speaker who, unlike executive officers, judges, and the actual members of Congress, had not taken an oath to the Constitution.