You're uncoiling the cord wrong, and twisting it as a result. 

Treat it as a spool. _Roll_ the coil to pull wire off it, don't just pull it off the side. Either roll the coil between the two points, or put a hundred through the center and pull the wire straight out in the same plane as the coil, _not_ from the side, letting the coil rotate as you do so.

Spooling is how it was packed, spooling is how it wants to be unpacked. Otherwise you will be twisting it, with the results you've seen.

(Digression into flipcoiling, which would allow pulling it straight out, deferred as tangential. Cable is _never_ sold as flip-coiled; spooling is far cheaper and easier to automate, and isn't a problem if you unpack it properly.)