This is true of any statistics, and I wasn't aware that anyone believed that big data was going to somehow eliminate subjectivity from the world. More data and faster processing means more opportunities to analyse and a bigger sample size, but as the adage goes, there are lies, damn lies and statistics. The article seems like a bit of a straw man.
And regarding myth 3 and 6: you can't really hold these views simultaneously. If you can opt out, then that's a built in form of discrimination. Whether that's actually relevant probably depends on your domain.
Many of the vocal cheerleaders have probably little experience or training in statistics, and so such nuance is beyond the scope of their understanding. Sure this seems self evident to those of us with the exposure, but think about all the folks who stop at college algebra.
It's true it isn't high-effort. That said, referencing xkcd (if not done solely for the humor) can be a nice way of succinctly presenting an idea that you would have made a mess of explaining yourself.
What I would gather from taking the article at face value is: According to Myths #2 and #3, big data is classist, racist and sexist. According #5 and #6, Big Data is actually Big Brother. #1 points out that Big Data isn't The Next Big Thing, because it's actually old news.
There's plenty of genuine problems with Big Data, but the article seems to be more concerned with playing on people's fears regarding it than actually providing any concrete arguments about its failings.
...but the hype cycle is and articles like this one are merely a product thereof. I really feel that opinion pieces ought to come from someone whose opinion is or should be highly regarded in a given field.