“Ski the slow line fast” still doesn't really make sense to me.i think "ski the slow line fast" is much more all encompassing than "complete your turns". IMO "complete your turns" is to vague, where as "Slow line as fast possible" is more abstract but not as vague.
I think I understand @bud heishman's explanation, but to me, line choice and speed are not directly connected in the way this phrase seems to imply. Obviously there are going to be lines that either require (in order to go back uphill) or demand (due to terrain) a certain amount of speed, but short of those exceptions, you should be able to ski any line at any speed, from the fastest physics will allow to a near stop. "Slow line fast", "fast line slow", or anything in between are all valid options. I don't really draw a sharp distinction between turning and braking, I see it as more of a continuum.
"Complete your turns" certainly requires some explanation. (If you're in the next turn, how did you not complete the last?) But I think @KevinF pretty much nailed it. It's basically saying, "be patient and work with the skis and gravity to maintain the speed and line you're comfortable with", which is very different from suggesting that one line choice or speed is better than another.
(So, basically what @teejaywhy said, but with a few more words. )
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