Why? In short, it is because Protestantism has historically believed the Bible is the Word of God and that it is important for people, including women and other minorities, to be able to read the Bible in their own language. This concern led Protestant missionaries to be catalysts for literacy, education, printing, newspapers, and so on, which in turn were mechanisms for the development of democratic rule. As he writes in the abstract
This article demonstrates historically and statistically that conversionary Protestants (CPs) heavily influenced the rise and spread of stable democracy around the world. It argues that CPs were a crucial catalyst initiating the development and spread of religious liberty, mass education, mass printing, newspapers, voluntary organizations, and colonial reforms, thereby creating the conditions that made stable democracy more likely. Statistically, the historic prevalence of Protestant missionaries explains about half the variation in democracy in Africa, Asia, Latin America and Oceania and removes the impact of most variables that dominate current statistical research about democracy. The association between Protestant missions and democracy is consistent in different continents and subsamples, and it is robust to more than 50 controls and to instrumental variable analyses.Woodberry's findings have been greeted with such skepticism that it has taken him several years to get his article published (I heard him present his results several years ago at a conference). Skeptical reviewers have asked him to estimate various statistical models that include a wide array of variables, certain that the inclusion of additional variables or estimating the models in different ways would cause the religious effect to go away. Woodberry even had to provide the assistant editor of the journal in which the article was published (American Political Science Review) with his dataset, the code he used to estimate his statistical models, printouts of all the models included in the article, tables from unpublished articles cited in the text, as well as five custom-made case studies that don't even appear in the article (these were necessary in order to allay the reviewers' doubts -- luckily, Woodberry will be able to publish them later in a separate article). Woodberry even plans to make the entire dataset available later this year so that others can replicate and test his analysis. In addition to the five sets of statistical models included in the paper, in an unpublished appendix Woodberry provides the results from 24 (count em') additional statistical models, all of which are additional tests of whether the religious effect is genuine or spurious.)
In spite of the best efforts of the skeptics, the religious effect never went away. In fact, Woodberry's results suggest that the presence of Protestant missionaries may have been the most important factor in the development of liberal democracy.
Why so many have greeted Woodberry's results with such skepticism probably reflects the state of affairs within much of the social sciences. For years, social scientists have been taught that religion doesn't matter, that any apparent effects it might display can be explained away by other factors (e.g., economic, social class). This belief was probably reinforced by the high level of irreligiosity among social scientists (in fact it is higher among them than it is among physical scientists); that is, because religion didn't matter to them, it made sense that it didn't matter for the rest of the world.
Because it just appeared in the May 2012 issue of the journal, the published version of the article is currently unavailable to nonsubscribers. However, an earlier version is ("The Missionary Roots of Liberal Democracy"). Better yet, you can listen to Woodberry being interviewed on Anthony Gill's Research on Religion podcast ("Robert Woodberry on Missionaries and Democracy"). Here's a brief description of the podcast:
Did Protestant missionaries help plant the seeds of democracy throughout the world? Prof. Robert Woodberry takes us on a historical tour-de-force around the globe showing how “conversionary Protestants” helped to promote literacy, spread printing technology, facilitate civic organization, defend religious and civil liberties, and protest the abuses of slavery and colonialism. We discuss how this happened and why Protestants were uniquely situated to do this, although we look at similar Catholic efforts in recent decades. We conclude with speculative thoughts about the Arab Spring.