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"Deduct" means to subtract, or take away.

"Deduce" means to logically follow evidence. Semantically, there's no overlap, whatever etymology might say.

This is one of those problems where spell check is correct, but the word is used incorrectly.

Wrong, "deduce" means to rule out possibilities, literally deduct them from the space of all possible universes.

"When you have eliminated the impossible, whatever remains, however improbable, must be the truth."

This is false. To deduce is to draw (ducere) a conclusion from (de) premisses.

Curios aside here: when pointing out a grammatical error of this sort, what school of English does it rely on? I mean, English has grown to a point where where the British English dictionary does not hold sole authority.

So do "fact"/"faction" and "hostel"/"hospital". Mixing these up would be confusing and incorrect. Seems like a silly argument to make.

'induct' and 'induce' are the same pairing, both are induction, and they mean different things. Saying someone was induced into the Army means something rather different from saying they were inducted.