I have heard versions of this argument that focus on management fees (based on the article this was Bernstein's point) and other versions that focus on there only being so much alpha out there.
It is not clear to me what Bernstein thinks of as long term but most indexers are talking about market cap weighting. If you recall last summer the ALPS Equal Sector Weight ETF (EQL) came out with a ten year back test of beating the regular cap weighted S&P 500. It should be noted that the ten year period backtested for EQL was probably the best possible time for such a thing because of excess and subsequent fallout of the tech sector and then the financial sector. I would also concede that Bernstein probably thinks long run is longer than ten years and I would not disagree with that but ten years of outperformance is a long time.
I believe I have made a reasonably compelling case on this site in the last few years for the importance of correctly avoiding a given sector or country. It does not take a lot of acumen to see that an S&P 500 sector is greater than 20% of that index which is a huge warning sign and easy to heed. Realizing that a country is on shaky ground takes a little more time but most certainly does not require a PHD.
Bernstein's point also ignores the fact that active management is a series of decisions; some right and some wrong. In this light success depends on being right a little more often than you are wrong. If the wrongs can be mitigated one way or another and the rights do well there is a good chance of outperforming. This point is difficult to win the argument with but as a supporting factor a stock I have been writing about for more than five years is Vale (VALE) which is a client holding. Vale as a proxy for materials is up 350% versus about 25% for the Materials Sector SPDR (XLB) in the last five years. This just an example which has flaws of its own but one (mega cap) stock pick combined with one sector avoided (the financials) and an investor would be noticeably ahead of the market for a decent chunk of time, that being five years.
I will say it is very reasonable to question how many people should be making a lot of active decisions in the market. People tend to not understand the volatility they have taken on until after a big decline resulting in panic sales so I am not saying everyone should be actively managing their portfolio but the idea of "has to by mathematical certainty" seems far too simplistic. I won't go into detail on another point here so the at post is not too long but another variable is the occasional buying and selling of stocks or funds that can add value as opposed to what I believe is a static portfolio in Bernstein's comments.
Bernstein also has choice words for levered and inverse ETFs, "But in practice, they’re being used as speculative tools. Some of them are silly, some are dangerous, and some, such as inverse and leveraged ETFs, are downright criminal" noting that they do not "work" over longer periods of time. He adds "what is this concept that an investment can only be used for one day? This is not an investment. Who has the predictive power of knowing which way the market is going to go on one day?" and finally "To the extent that people are using them more for speculation than for long-term investment, it’s a horrible thing."
I would not disagree with an opinion that says many people will misuse a levered fund but speculation plays an important role in the functioning of capital markets. I think this is a rather elementary point actually--markets need liquidity to function and speculators are a source of liquidity. Again any argument that says most people should not be speculating is one I would agree with but the framing that speculation is a bad thing and tools that facilitate speculation are bad things is, again, too simplistic.
To the extent new investors are trying to learn and seek out Bernstein as a source I believe they are learning the wrong thing. There is a difference between a fund being "downright criminal" and a fund simply being unsuitable for many people.