The concept of things increasing in value with small probabilities is well-known. Words used for this concept include: good luck, lottery tickets, a home run, teenie (a low-delta option), eureka moment, ten-bagger (a stock that can increase in value ten-fold). Having good luck, winning lottery tickets, is great, but how to achieve this is not straightforward, and certainly not simply by being long lots of them.
Lots of investments offer large returns with low downside, why penny stocks and long option positions have lower-than-average returns (and distressed assets are not better-than-average), as lazy investors chase instant riches. Contra Taleb, it is not the quantifiability of lottery tickets or the fact that they have a maximum payoff, that makes them bad investments: things with lottery-ticket type qualities with uncertain parameters such as internet business opportunities are generally a fraud with a poor expected return, and things like IPOs, or analyst disagreement (which have more of what Keynes and Knight called 'uncertainty'), are intuitively riskier and have lower-than-average.
He doesn't identify key attributes of attractive antifragile opportunities, just implies they are the ones that unlike options and lottery tickets, work well. In fact, he's anti-theory, so one supposedly finds them by random sampling (aka 'trial and error'). That's a strategy statistically proven to underperform, catering to the biases most investors have, why both day trading bucket shops thrive and low volatility investing works. As a self-help book it's like someone saying you should eat more sugar, a strategy many will find highly convenient.
The book is really a big spread argument that it's good to be long gamma, bad to be short it. Gamma is the essence of an option, why there's 'time decay' or theta, a predictable expense that anticipates the payoff times the probability. Whether or not this theta is adequate for the gamma is whether an option is priced fairly or not, and generally people pay too much for gamma, why historically the VIX has been about 1% higher than the SP500's actual volatility, and this implied volatility bias has been even higher in the tails. Being long options (positive gamma), especially out-of-the-money options, has been a losing strategy.
One key to understanding Taleb is the Freudian concept of projection: he applies his greatest faults to others. For example, he defines the "Joseph Stiglitz problem" as cherry-picking his prior statements to claim they predicted something when they did not, referring to Stiglitz's ill-fated Fannie-Mae prediction and subsequent recollection of calling the 2008 financial crisis in a later book. Yet Taleb himself did the same thing, as he criticized Fannie Mae for not understanding the embedded interest-rate option in their mortgage portfolio, but then claims he accurately predicted Fannie's failure. Prepayment risk is very different than collateral risk, and Taleb mentioned nothing about collateral risk prior to 2007, and instead alluded to the prepayment option problem. It's like a guy who says corn prices might increase because of risk from floods, and when a collapse in the dollar causes it's price to rise, states, 'I told you so.' Hindsight bias, name dropping, hypocrisy, and pretentious mathematics are Taleb signatures he sees everywhere in others.
Another key to understanding Taleb is that he has a French post-modern style, writing to impress rather than explain. He provides hundreds of loosely related anecdotes, reminding me of the Talmud quote that 'when a debater's point is not impressive, he brings forth many arguments.' One can find a lot of Taleb to agree with, but only because he says so many inconsistent things.
Then there are the many confused or dubious assertions. For example, how can one be sure that Black Swans are both impossible to quantify and highly rewarding? Isn't that untestable? Isn't Popper one of his favorite philosophers? Do most economists and risk managers really not understand that the function of an expected value is not the same as the expected value of a function? His absurd equation for fragility has a couple of subjective parameters that would make them impossible to compare one strategy or portfolio to another, and equations with unknown parameters are like bad haikus, or rather, very helpful if you want to impress the mathematically challenged.
Taleb often suggests it is good to be long volatility, things that gain from greater uncertainty (see his YouTube on this here). As the VXX has shown, while this has nice covariance properties with the stock market (going up in 2008), it has a horrible long run return. I bet many of the unfortunate investors who have ridden the VXX to zero over its existence have a copy of The Black Swan on their bookshelf (and you can extrapolate it backwards, and even if it started in 2006 it would be a loser). The 'long vega' bias simply isn't a good one unless you qualify it more concretely.
He notes there's a sweet spot for most medicines, and that some exercise is good for you, not in spite of its stresses, but because of them. But if the key to benefiting from the 'right' amount of medication is dosage, how does one find this dosage? Trial and error? That's how most animals learn, but it's pretty inefficient in general, I certainly don't want my kids figuring out most of their life lessons that way, because it's very time consuming and costly. Surely, a 'moderate amount' of trial and error is essential in everything, so one is left with nothing.
He still thinks Portfolio Theory, and most Economic Nobel Prize winning research, is predicated on distributions with fixed parameters. It isn't. Further, as much as he hates the Nobel prize in economics, he doesn't hesitate to put its imprimatur on the back blurb of his book (a recommendation from Danny Kahneman--Nobel Prize Winning Economist it notes prominently).
As per correlations being stochastic and so uninformative, he is wrong again: they are highly predictable, as high beta portfolios formed using past data create portfolios with higher future betas. The same is true for low volatility investing. They aren't perfectly predictable, nothing is, but that's really a straw man argument.
A good amount of gamma or convexity, like having just the right amount of medication or specialization, is a good thing. Yet the right amount can be positive, negative, or zero, in various contexts. Many good things have negative gamma, such as the strategy of being nice to strangers: it has great downside, such as when you naively interact with an aggressive stranger, yet being nice is a good default strategy. Then there are things with no gamma, such as brushing your teeth everyday or simply being polite, which generally doesn't have a lot of effect either way in your life any time you do it, but over time is quite salubrious. Noting gamma per se, especially large gamma, doesn't tell you if something is good or bad, rather, just that it could be really good or really bad.
You can price gamma and it's not free, so the question is always whether this price is too high or too low. How do you price things that respond hydra-like to having its head cut off? He doesn't talk about how to identify undervalued opportunities, and instead encourages people to keep doing what they've always done, waste money on poorly researched lottery tickets (oops, Black Swans).