Let it be said: people will always complain about arithmetic techniques other than what they were taught as children, and those complaints rarely go beyond "but that doesn't make any sense!" because people are bad at math and memorise techniques rather than concepts. This should be sorted out by actually testing which method works better, not through facebook outrage which isn't even aimed at the right thing.
That being said, I'm not terribly convinced by the arguments for the new way. First, it seems much slower (subtracting two-digit numbers takes 8 sums as opposed to two subtractions, in the example given, thought it would vary with the specific numbers). You might argue that the purpose of teaching kids pen-and-paper arithmetic is to understand the underlying concepts rather than get it done quickly, which is what calculators and computers are for, but decent methods of pen-and-paper arithmetic should also have a place in education. Sometimes you don't have a calculator on hand.
Second, there's a false equivalence between understanding subtraction and understanding the subtraction algorithm. Yes, it's a bit harder to see how the old algorithm is implementing subtraction*. That's not the same as students not understanding what subtraction is.
Third, the article shows a picture from reddit that shows how much easier it is to do 3000-2999 the new way. Sure. But that's not the kind of calculation you do on paper, anyone can work that out in their heads. The "new way" is similar to how we carry out mental maths on simple subtractions, so it's redundant to teach it instead of the new way.
But, words are wind, data is solid**. Like I said, test both methods and see what happens, teach whichever works best (or both, if they are good at different things).
*I think, anyway. Both methods are pretty clear to me, but I'm a maths nerd and I'm not very good at predicting what the average person understands of maths.
**I need a better saying for this. None comes to mind.
Edit: Also, because it's appropriate and I like Tom Lehrer. Visuals aren't the best, but most videos lack the first part of the audio.