Many, many reasons, some as simple as the climate: most industrial products, including the principal industrial good of the time, textiles, need to be produced indoors and indoor labor was extremely difficult and dangerous in the Southern heat before air conditioning.

Historians of the antebellum period will often also point to sundry geographical factors like the soil in New England, the speed of rivers which provided cheaper power to mills and the much better ports for shipping textiles to overseas markets. They'll also point out that, for broader historical reasons, the local consumer in the South was much poorer than his equivalent in the North—on average—and so there was far less of a local market incentive to produce industrial goods.

Industrial labor also tends in various intangible ways to favor cheap, but not necessarily free, labor: most of it requires more skill than agricultural labor and profits rely on the ability to fire slow or underperforming workers. You can do that with European immigrants but it's a lot harder with slaves. Cursory examinations of the economics of slavery, in fact, often downplay this hugely important tradeoff: slaves were very, very expensive (many small slaveowners owned them with a mortgage) and had to be fed and housed, however minimally. If one didn't perform, his owner had to eat the loss. A factory owner needed constant reinvestment and couldn't afford to do this—but he didn't have to pay upfront for Irish immigrant workers or provide them room and board.

In general because of this discrepancy in the source of labor, the slave economy tended to be very conservative, both short- and long-term. Planters had invested enormous portions of the region's wealth into slavery-based agriculture, and even if the conditions were better it would have been difficult to persuade any of them to shift that investment to manufacturing with its high upfront costs.

It's all a rich tapestry, and all these factors combine. The only one I'd warn against is the notion that "culturally" Southerners didn't like fancy new machines for some reason, a common explanation that's easily refuted by the facts and smacks of cultural chauvinism.

Please understand that my answer will only address a few of the complicating factors. Though I've never really thought about it, /u/tetuphenay does bring up an interesting thought experiment about indoor manufacture and heat, but I'm not sure I'm convinced. So here's my take from about 6 years of teaching university level American history (upper and lower division):

It comes down to motivation and economic need. First, plantations were immensely successful in the region we'd like to call the "South" - Virginia, The Carolinas, Louisiana, Mississippi, and Alabama, for example - and a large chunk of the land was devoted to agricultural production, primarily of cotton. Comparatively in the area we'd like to call the "North" (say, New York, Massachusetts, Pennsylvania, and Ohio, for example) there were more holdings held by relatively smaller landowners who concentrated more on edible agriculture than cash crops. This difference alone makes land relatively cheaper or easier to purchase.

Add to that the historic mercantile community which grew up mainly (though by no means exclusively) in the North and you have an environment conducive to risk-taking, entrepreneurial ventures which really doesn't exist in such a robust way in the South. As Alan Brinkley points out in his textbook Unfinished Nation, there is a gravitation toward industry in the North while the social and economic wealth brought by agricultural exports in the South discouraged such innovations. The South really had a lot going for it economically; Britain paid a good price for cotton and to sacrifice valuable land for untested and untried (and unprofitable) industries just made no financial sense. Even the North was largely invested in the South remaining undeveloped (industry-wise) as Northern textile industries purchased cotton cheaply in an effort to compete with their British rivals (the later of whom were flooding American markets with cheap, well-made goods); look no further than the rhetoric surrounding the Nullification Crisis of 1832 where South Carolina (and some Northern merchants) worried the protective tariff placed on British imports would be reciprocated by the British making US cotton more expensive and thus not attractive enough to buy. Carolinians such as Henry Clay nearly rent the country over the issue of cotton exports largely because there wasn't enough industry in the South to take over for the (potentially) lost profits from cotton export. But I digress.

That's not to say that the South was without industry at all. In fact, major cities did have manufacture and processing, including arms manufacturing facilities (rather convenient when the war broke out) in places like Charleston and Atlanta. And they did have lots of railroads, though not nearly the raw mileage that the North had and most were pretty much directed towards port cities like Charleston and New Orleans or markets in the North.

As for population density, yes, the North had a lot more people living in it for a variety of reasons; availability of low- or unskilled jobs, ethnic enclaves (ghettoes), as well as relatively cheaper land to name a few. Culturally, some Europeans (such as Germans) were repulsed by slavery and shied away from settling in places where the issue of slavery could get you ostracized or even killed (see: http://www.tshaonline.org/handbook/online/articles/png01 ). Some, of course, were more ambiguous about slavery and so either settled in both North and South (such as the Irish) or favored the South (many French Zouave soldiers) but comparatively, the immigration to the South was much more light than to the North. This contributed heavily toward the North's numbers. Also, the North was able to recruit some other country's citizens to fight on its behalf, such as Union recruiters hiring Canadian sailors or British, German, and Italian mercenaries to lead the North's armies. The South had the majority of bright commanders and a dedicated cadre of troops and so wasn't as successful or interested in recruiting abroad.

As for inevitability, we have to be really careful here: historians do not like the term "inevitable" and that is particularly true in the case of the Civil War. Remember, the South was actually winning (or at least succeeding in stymying the North) during most of the Civil War. Generals like McClellan were a bit too cautious or not active enough while others were outright inept or frauds (or both), costing the North mightily in men and war materiel. Grant was one of the first few successful Northern commanders, but is a controversial figure because he used a LOT of troops to accomplish his goals - a war of attrition the South could ill afford to wage. The combination of that, plus Sherman's scorched earth policy, plus the emancipation proclamation, plus the decision to allow black to fight all helped the North in the long run. But the South was not "destined" to lose. In fact, if it were not for a few bad decisions on the part of the South, it is entirely possible we'd have two united states today.

Some decisions, such as refusing to allow blacks to fight, as well as quibbling over the war (some states refused to allow their troops to become part of a larger army of the Confederacy) hamstrung the South and, coupled with the advantages noted for the North, pretty much sealed the fate of the South.

I hope that sheds some light on the divide in question and I'm sure any moment now some of the US historians will chime in to correct, update, or add to my post, so if I missed anything, I'm sure we'll have it covered soon.