Whole books or libraries have tried to address this problem, and there is no perfect answer, but I will outline what I consider to be at least one of the most complete and convincing analyses, given by Kenneth Pomeranz in The Great Divergence. Texts that may be familiar in addressing this problem include:

• The aforementioned Pomeranz, which is quite scholarly and at sometimes difficult to fully synthesize because he wisely makes use of many caveats and contingencies.
• Ian Morris' Why the West Rules... For Now, which is written more for a popular audience and probably gets the broad strokes right, but is too cursory in places and oversimplifies many of the specifics of industrialization that Pomeranz outlines in greater detail.
• The much-maligned Guns, Germs, and Steel, which again has elements of a convincing thesis, but drastically oversimplifies many of the core issues, and is straight-up wrong in its oversimplified analysis of China vs. Europe. In essence, the book makes a reasonable case for "why Eurasia and why not the Americas," but it's far less convincing on "why Europe and not China or India." Read up on the FAQ for the specific critiques of this work, which I will not mention further.
• Civilization: The West and the Rest by Niall Ferguson, which credits "the west" (a term that Ferguson re-defines or fudges in a number of places) with six "killer apps": competition, the scientific method, the rule of law, modern medicine, consumerism and the work ethic. In my opinion this is pretty boilerplate, unsatisfactory, and contains too many shifting goalposts to be convincing. But it is also written for a popular audience and offers an explanation, though not one I'm particularly satisfied with.

There are many others who have attempted to address this problem, but that's a brief overview of recent (last 20-25 years) major works. So with that out of the way, let's summarize some of Pomeranz's argument, in brief:

1. On comparisons: Pomeranz finds that comparing China to individual European nations is problematic and inexact because of profound size differences, and that comparing China to Europe as a whole is problematic because of the tendency to obscure political and cultural differences. Therefore, he aims for geographic specificity and tries to compare similarly-sized or similarly-structured regions, like Britain vs. the Lower Yangtze valley.
2. Ecology: all societies face a problem of resources in their development; in order to obtain the intense specialization needed to sustain industrialization, there must be a sufficient surplus of food and raw materials to supply workers and consumers who are not themselves direct producers. Europe, India, and China faced relatively similar ecological constraints and faced problems at the margins prior to about 1700 that prevented them from further development. But Europe did have the advantage of access to New World resources, not only for raw material, but as an outlet for both surplus labor and ready markets for their goods. Pomeranz is hardly the first to argue for the critical role played by New World access, but he expands considerably on other explanations he considers overly simplistic, such as Marx's "primitive accumulation" of capital theory. Just crediting the conquest of New World societies and the plundering of their mineral and ecological resources is insufficient, but it is an important factor.
3. Market Hypotheses: Pomeranz also critiques the "institutionalist" argument that suggests that European foundations of markets built on strong property rights and competition account for the presence of capital forces needed to undergird industry formation (these factor heavily in Ferguson's aforementioned argument). He makes a fairly convincing case that in terms of the "perfect markets" of informed consumers imagined by Adam Smith, China might have been a more "free" market than most European states, which intervened heavily through mercantilist economics, state-granted monopolies, various forms of coerced labor (serfdom, slavery, etc). Instead, Pomeranz suggests that as late as 1750, both Europe (especially Britain) and China (especially the Yangtze Delta) enjoyed relatively similar levels of "proto-industrial" development, i.e. expansion of "nonmechanized industries, mostly composed of rural laborers producing for distant markets through the mediation of merchants" (Pomeranz, 21).
4. Agricultural Markets: However, when considering (2) and (3) side by side, Britain had ready markets for its proto-industrial cloth in its colonies and peripheral states, while Yangtze cloth producers had trouble finding adequate markets for their products, not because of any "flaw" in Chinese economics, but because their chief areas of export were not agriculturally-specialized colonies, rather they were other proto-industrial areas of China (Pomeranz divides these into 8-9 macro regions, each similarly large to typical European states). To quote Pomeranz again, "a combination of inventiveness, markets, coercion [especially in the form of the slavery-plantation complex], and fortunate global conjunctures produced a breakthrough in the Atlantic world, while the much earlier spread of what were quite likely better-functioning markets in east Asia had instead led to an ecological impasse."
5. World Systems: To further expand on (3), Pomeranz argues that a lot of the factors that would seem to credit European ingenuity and market formation relied significantly on extra-European factors. All of that New World silver would have been valuable, but not nearly to the same extent had China not re-monetized its economy based around silver in the 15th century, before any European set foot in the New World.
6. Fossil Fuel Technologies: With regard to technology, Pomeranz again stresses that up to 1700 or even 1750, Europe, the Ottomans, India, and China all had access to the tools needed to build industrial machinery: metallurgy, monetized economies, agricultural markets, knowledge of pistons and turbine engineering, etc, but distribution of fossil fuels was not as even across societies. Again, Britain enjoyed an advantage here, as being relatively small, the proximity of coal to growing industrial centers and then to urban cores formed a virtuous circle. In China, the journey was more arduous, as the Lower Yangtze Valley did not have comparable coal deposits, though China as a whole had probably been longer and more prevalent users of coal than Europe. For somewhat idiosyncratic reasons (based in part on geography and invasions of China from the North), the coal sector was somewhat isolated from various industrial centers at this critical moment. Furthermore, England's coal mines further stimulated some industrial technology because mines frequently needed to be dredged. Coal mines in northwest China, by contrast, were too dry, and needed "ventilation rather than powerful pumps" (Pomeranz, 65).

That's a lot to take in, and Pomeranz's argument is incredibly complex and nuanced, so a closer reading is definitely encouraged, as I cannot fill all the gaps here. But if we have to produce a few takeaways:

• Contingency is important, and we should be skeptical of arguments that are reductive down to the level of culture, since Europe and China in particular were at relatively similar levels of economic and technological development as late as 1750.
• Geography is important, but not a singular factor (which is a major reason why analyses like Diamond's fall flat), and not always in the way that people would think.
• Access to the New World was an important factor for Europeans, but one that would have been incomplete without proto-industrial development, established maritime trade, and monetized economies in India and East Asia.
• Political competition among European states was probably a factor, but cannot on its own explain the technological drive among European engineers and inventors.

So on the whole, we should be pretty skeptical of any singular factor, and Pomeranz spends almost as much time critiquing others' arguments as he does developing his own, and for good reason.

I can try to follow up some of the specific areas in your question ("geographical, cultural, demographics, economic, and political factors"), but probably the best thing I can do is point to works that deal with this question in more detail. I would encourage other posters to add reading recommendations, but The Great Divergence is a good starting point for addressing this question, and for gaining some insight into the historiography of this problem.