It comes from the Latin "laevus".

Funnily enough, although "sinister" came to mean "the bad side", it may have come from Proto-Indo-European for the "favourable side".

In politics in the UK, there is a left and right side of the "house". Currently the Conservatives are the right and Labour are the left. Neither party existed when the UK Parliament was initially created.

I wonder whether the old Latin (right == good/left == dodgy) thing has been perpetrated here or it it is coincidental.

I also wonder whether old Latin speakers really had a snag with sinister ie left handers or is that a modern affectation.

Knowing that ambidextrous thus means "both right (hands)" makes me marvel at how such a brazenly politically incorrect figure of speech has for so long remained undetected by the cultural police thanks to a linguistic camoflauge that mimics medical-sounding jargon.