1. It presumes when you have achieved product-market fit. The supporting example was about measuring success of products over time. iPods did not sell as fast as iPhones, and on that basis Apple should not have introduced other iPod models after iPhone.
This argument is flawed because, first Apple is not a startup. Second, and most importantly, Lean Startup never said that one should use metrics from another products to assess the product-market fit of a product. In the example, exactly because of the risk of cannibalizing iPods, Apple decided to introduce new models (i.e. to do a pivot, as Lean Startup suggests).
2. Lean Startup presumes that once you have product-market fit you can't loose it. The supporting example, is Netscape that once had the product-market fit, but lose it when Microsoft included Internet Explorer in the OS.
Again, the fallacy resides on the fact that Netscape was not a startup. But more importantly, this was not a problem with customers needs, but rather than an external factor that forced the users to accept Microsoft policies/strategies. Horowitz points out that they "did not have the luxury to address the issue in the Lean Startup way". That's not a "luxury", is a rational way to adopt if a company cannot afford to splash milions for crashing new product development. Actually, it is the Fat way a luxury that startups cannot afford. In such a case, Lean provide a way to achieve decent results with a fraction of "Fat" resources.
3. Lean startup implies or assume that there is no competition. What if prior achieving product-market fit, even if the market is large, a scary competition appears. The supporting example is taken from VMWare who take care to invest money in order to be ahead of open-source competitors like Xen and big scary competitors such as Microsoft.
The argument is obviously fallacious because, first not even VMWare was a startup, but secondly because if crashing massive resources to gain competitive advantage works well, this does not necessarily mean that Lean doesn't. When it is not possible to deploy brute force to deal with competitors, Lean offers smart tools (like David and Goliath). One idea is to elicit niches where competitors are weak or not considering so that the startup can avoid direct competition and possibly erode the main market. Lean Startup is in that sense compatible with the work of Christensen's work on disruptive technology and emergent markets.
The problem with Horowitz is not business skills; it's LOGIC. He provided three fallacious arguments against Lean Startup. I also believe that Lean is not universal and there are many contexts where it does not apply well (e.g. large established companies for mainstream products). Also, Lean Startup advocates that once the business scales, the conditions change and probably the methodology is no longer applicable.
Besides, a Fat startup model has several problems, among which "premature scaling". Horowitz was unable to explain how the Fat model could be beneficial for startups as he showed only Big Companies examples.
On the other hand, the Willson's argument was much clearer and plausible:
"Wilson’s argument focused more on how to maximize the probability that entrepreneurs will get favorable exits. He boils down the formula to: (Founder’s Stake) x (Probability of an exit) x (Size of the exit). Wilson says to focus on the first two variables. Accepting more funding will dilute the founder’s stake, but it isn’t going to proportionally increase the probability of an exit (which is based on far more factors). In other words, it hurts the likelihood of a favorable outcome (at least from the entrepreneur’s perspective). Likewise, he says investors are looking to mitigate risk, which is why investing small amounts when a company is young is in their interest."
However, he only focused on one of the many benefits of the Lean Startup model: the reduced need of initial resources. Lean Startup is a comprehensive methodology that make sense for startups (possibly with a few exceptions), and it has several facets.
My personal opinion is that Lean Startup can help startups in finding the right direction towards a sustainable, profitable business model by incorporating failure in the product and market development process. Failure becomes a learning event, which allow the startup to "rule out" the failing paths (or pruning, to use a Computer Science terminology, the "dead branches" of the business opportunity search tree) very early in the process.