The CDC brief is by a US government department and cites 45 studies to back up its recommendations.
The article you posted above it cites one study, and is written by a privately run libertarian think-tank. I feel it's important to mention that the author's opinion mentioned above was from the FEE.org article's author, not the study that it cited. The Danish study referenced closes with these two paragraphs - I've underlined portions, but I feel it's all worth reading:
Our results suggest that the recommendation to wear a surgical mask when outside the home among others did not reduce, at conventional levels of statistical significance, the incidence of SARS-CoV-2 infection in mask wearers in a setting where social distancing and other public health measures were in effect, mask recommendations were not among those measures, and community use of masks was uncommon. Yet, the findings were inconclusive and cannot definitively exclude a 46% reduction to a 23% increase in infection of mask wearers in such a setting. It is important to emphasize that this trial did not address the effects of masks as source control or as protection in settings where social distancing and other public health measures are not in effect.
Reduction in release of virus from infected persons into the environment may be the mechanism for mitigation of transmission in communities where mask use is common or mandated, as noted in observational studies. Thus, these findings do not provide data on the effectiveness of widespread mask wearing in the community in reducing SARS-CoV-2 infections. They do, however, offer evidence about the degree of protection mask wearers can anticipate in a setting where others are not wearing masks and where other public health measures, including social distancing, are in effect. The findings also suggest that persons should not abandon other COVID-19 safety measures regardless of the use of masks. While we await additional data to inform mask recommendations, communities must balance the seriousness of COVID-19, uncertainty about the degree of source control and protective effect, and the absence of data suggesting serious adverse effects of masks.
The CDC's conclusion is, in part:
The relationship between source control and personal protection is likely complementary and possibly synergistic, so that individual benefit increases with increasing community mask use. Further research is needed to expand the evidence base for the protective effect of cloth masks and in particular to identify the combinations of materials that maximize both their blocking and filtering effectiveness, as well as fit, comfort, durability, and consumer appeal. Adopting universal masking policies can help avert future lockdowns, especially if combined with other non-pharmaceutical interventions such as social distancing, hand hygiene, and adequate ventilation.
The problem at hand is that when it comes to community disease control, any strategy is only as effective as the population's efforts to implement it. The Danish study emphasizes that it was based on a smaller subset of a population wearing masks vs. the majority not doing so, while the CDC's conclusion is that available data points to an increase in overall effectiveness when a higher percentage of the population participates in mask wearing, and more importantly, the other basic measures that people can (and should!) take in conjunction.
It is very easy to pick a few lines from a single study out of context and claim that it's scientific proof of one's desired point. I don't see how one can make claims from this one study (that itself came to no definitive conclusion), while at the same time ignoring data from 45 other studies and the CDC's conclusion that points to them at the very least being useful in conjunction with other measures. If people are ignoring the other measures, then that's not a mask problem. That's a 'people are stupid' problem, and should be rectified by, instead of attacking masks and the evolving data surrounding them, pointing out and correcting those people's irresponsible behaviour. Letting those same people instead make random, poorly informed decisions about what precautions they take, regardless of their impact on others, and expecting that to somehow pan out better for the populace doesn't seem logical to me.
If, eventually, it can be conclusively proven that people wearing masks worsened the pandemic, then by all means get the tar and feathers for me. Just wash your hands first...