[Chris2048]

Yep, and to explain further; The first instance of "ruling" in a judicial sense probably derives from rule (i.e dictat/maxim).

To "rule out" is to use a ruler to cross a line through something in a written list of items, thereby eliminating it from consideration.

[wccrawford]

But also in colloquial English, "rule out" means "eliminate by logic". Like, "use the rules to take it out of possibility".

[dan-robertson]

I don’t think this is an accurate definition or etymology. The phrase can mean “formally remove” or just “eliminate”. I think it always alludes to using a stick of wood to draw a line rather than a regulation or law.

[wccrawford]

My etymology might be completely wrong. No argument there.

But as for the meaning, that's what it's always meant when I've heard it said. So it definitely means that, at least colloquially.

[zeroimpl]

Definitely agree here. I’ve never associated a physical ruler with the verb rule.