I know the Manchu Qings overthrew the Ming Dynasty and replaced it with their own dynasty, but why did the Chinese people hate them so much? I've heard most people say some of the hate was because they were Manchu and so they were 'foreign invaders', but Manchuria is part of China, right? So how could they say the Manchus were 'foreign invaders'?
To correct a misconception here, Manchuria has not traditionally been part of China, and with the exception of the Liaodong Peninsula its population was never majority Han Chinese before the later 19th century. Hence the Manchus being considered foreign invaders – they were.
So why was there opposition to the Manchus? Obviously there were a vast number of reasons, but the most salient ones would probably be:
##Anti-Manchuism
When discussing anti-Manchu sentiment under the Qing it is important to distinguish between two main types: the cultural anti-Manchuism that dominated the discourse up to the mid-19th century, and the racial anti-Manchuism articulated in one form by the Taiping and in another by Social Darwinists like Liang Qichao.
The Ming Dynasty had seen the solidification of notions of Chinese cultural supremacy to a very literal extent. The failure of the Ming to project into the steppe had resulted, eventually, in the construction of the Great Wall, which saw retrospective justification as a necessary measure to isolate civilisation from barbarism. Behind the wall, the Ming established what we now call the 'tributary system', a network of formalised, ritualised gift exchange-based relationships between the maritime powers of East and Southeast Asia – the key 'partners' being Korea, Viet Nam and to a lesser extent Japan, all of which might be termed part of a broader Early Modern 'Sinosphere'. In this atmosphere, a growing sense of superiority over the steppe 'barbarians' was a pretty inevitable consequence of the self-assurance of the Ming court.
The Manchu conquest, therefore, was a severe blow to the notion of Han Chinese cultural supremacy. While imposition of the Manchu language broadly failed at first and was not seriously attempted, the imposition of Manchu dress and, crucially, the Manchu hairstyle, were enforced by threat of capital punishment and in turn viciously opposed. The degradation of being made to adopt a steppe hairstyle was severe enough that many preferred capital punishment, or in some cases opted to become monks in order that they could shave entirely. Anti-Manchu critiques based on notions of Han cultural supremacy remained significant until the mid-18th century, with the last high-profile case being the Zeng Jing conspiracy of 1728.
The 19th century, however, saw the emergence of a new critique of the Manchus based on racial categorisation. In the 1850s, Taiping propaganda claimed that the Manchus were descended from animals and that general miscegenation between the North Chinese and barbarians over time had left the South Chinese as the only ones who could truly restore China to its pure, monotheistic roots. Subsequently, intellectuals in contact with Western notions of scientific racism blamed China's weakness to foreign invasion on the inability of its foreign ruling caste to integrate – literally – into the Chinese population writ large, and asserted that the Qing empire could only survive if it allowed the Manchus to become assimilated into the Chinese population through miscegenation.
##Problems of Local Government
No dynasty, particularly after the Mongol Yuan, was ever able to rule except through extremely close cooperation with local gentry. Some members of the gentry joined the literati scholars who staffed the imperial bureaucracy, others remained in their locales and became crucial to local government by offering their services to, and leveraging their social capital on behalf of the bureaucrats. Through the later imperial period the gentry increasingly consolidated their landholdings, with one crucial innovation being the development of 'topsoil' and 'subsoil' land ownership – the former entitling someone to build and work on land, but only by paying rent to the subsoil owner. The prevalence of tenant farming could vary heavily (most land in Shandong was still operated by freeholders as late as 1900, whereas Hong Kong's rural villages in 1898 were primarily tenant-farmed), but it illustrates a wider trend of growing gentry power. This in turn led to two distinct responses, both anti-Qing.
One response, largely by poorer peasants increasingly constrained by gentry land consolidation, was to oppose the Qing for its failure to guarantee the livelihoods of ordinary farmers. The emergence of local mutual aid organisations and secret societies can be seen as an underground response to the failure of the Qing to prevent elite overstretch. Societies like the Nian in north China and the Heaven and Earth Society in the deep south provided organic means of gaining redress against gentry abuses which the Qing state was failing to provide. Subsequently, as the Qing's ability to provide security deteriorated in the wake of revolts like the White Lotus uprising and later on the Opium War, secret societies further capitalised on the power vacuum in local administration by offering military protection against bandits – societies profiting from such measures included the God-Worshipping Society (which became the Taiping) and the Small Sword Society. These societies frequently rose up, many with intent to overthrow the Qing state entirely, due to its simple failure at countering growing landlord power.
Conversely, the gentry sought to expand their power on the basis of their growing local authority. A school of thought called fengjian (lit. 'sealing and construction') advocated a partial reversion to Zhou-era feudalism by essentially dividing the countryside into hereditary fiefdoms. The landlords with their fixed abodes, its advocates argued, were more attuned to local interests than the district magistrates, who were rotated out every couple of years and would have to cooperate with the gentry anyway, so why not get rid of that bottom tier of magistrates, and just let the gentry do their own thing? While somewhat of a fringe position, it was only the extreme end of a general spectrum of support among the gentry for increased decentralisation. Even hardcore Qing loyalist Zeng Guofan promoted gentry above imperial interests when he began his post-Taiping reconstruction programme in Nanjing, prioritising literati infrastructure like examination centres before key imperial sites like the Ming tombs. After the Taiping, the political philosophy of constitutionalism, championed in a moderate form by by Kang Youwei and in a radical form by Liang Qichao, continued this trend by proposing a system of government in which the gentry had a greater and more officially-recognised hand alongside the emperor, while republicans like Sun Yat-Sen argued for a completely gentry-led government chosen by a limited, property-holding electorate. By 1911, the growth in gentry power and the weakness of the Qing (which to some extent went hand in hand in a sort of snowball effect) had made it viable for even the conservative rural gentry to decide to allow the Qing to be overthrown and a new, landlord-dominated republican government be put in its place.
##Modernisation and Imperialism
Later in the 19th century, consciousness of the Qing empire's precipitous decline in geopolitical status spurred on a major effort to reinvigorate China. Disagreement came, however, over whether a 'modernised' China had a place for the Qing. Gentry conservatives like Li Hongzhang and moderate constitutionalists like Kang Youwei certainly thought so, but post-1898 radical constitutionalists like Liang Qichao and republicans like Sun Yat-Sen generally thought otherwise. Part of the question was whether the Qing were holding China back, or whether a maintenance of the established Qing government was neccessary for progress because an attempt at replacement would simply invite further catastrophe by stoking internal divisions. While Liang Qichao's polemics about the Qing's failure to miscegenate were an explicit racial critique, they also came in the context of a broader argument that, at least in its current form, the Qing was an obstacle to Chinese progress, and that further encroachment from foreign powers would be the inevitable consequence if there was not radical reform as quickly as possible.
Speaking of encroachment, foreign erosion of Chinese soveriegnty was generally not considered a major salient issue until at least the 1880s. The Opium Wars were to some extent barely a blip on the radar in the eyes of most ordinary Chinese, and from a government standpoint had to be seen in the context of broader frontier relations, particularly with Russia, the Khanate of Kokand and Viet Nam. The severe loss to Japan in 1894-5, however, sparked a major moment of introspection about the future of China, which led some to support reform (most notably the botched constitutional movement of 1898), some to advocate hardline reactionism (particularly the pro-Boxer court factions), and some, increasingly, to entertain overthrowing the Qing entirely. The 1911 Revolution, for example, was precipitated over controversies about foreign ownership of railways and their attached land rights, but over time ballooned into a general move to overthrow the Qing and assert rule by the Chinese provincial landlords.
##Conclusion
With everything taken into context, it must be said that imperial encroachment was far from the only issue at hand, and far from the most important. Rural opposition to the Qing in the first decade of the 20th century more often than not was due to the New Policies, a set of measures that were widely seen as gentry-empowering and essentially a Qing sanction for oppression of the peasantry. The appointment of the 'Princes' Cabinet' by the regent Zaifeng in 1909 did much to erode goodwill regarding planned constitutional reform by confirming fears of not only imperial, but crucially Manchu recentralisation. And of course the elite had their own political interests in seeing the dynasty fall. In all, the fall of the Qing Dynasty was ultimately the result of its domestic troubles, not its foreign ones.
They didn't, initially. The Qing were extremely powerful and popular for most of their rule.
The events of the Nineteenth and early Twentieth Centuries, however, were widely seen as emasculating by the people, as well as damaging to China's prosperity. Economic and political expansion by foreign powers, particularly but certainly not exclusively the British, weakened the Chinese state. The British orchestrated an opiate addiction crisis that wreaked havoc on the populace. The Japanese, thought to be a smaller power at the time, humiliated China in the first Sino-Japanese War.
These humiliations lead to the Boxer Rebellion, where many were swept up in a violent populist movement targeted against foreigners operating in China. The Qing ultimately join with the Boxers, but it is too little too late. An eight-nation force not only obliterates the rebellion and the Qing force, it also takes many priceless heirlooms of Chinese history (again, mostly the British).
The Qings managed to hold on to power for another decade after that, but it was basically a dead dynasty walking. The Manchukuo puppet state obviously didn't help their popularity, but they had been out of power for a long time at that point.
Finally, while I wouldn't say that ethnicity was anywhere near the major contributing factor, the Qings were not ethnically Han. 95% of the Chinese population is ethnically Han. So, while Manchuria was and had been a part of the empire, they were not of the same ethnic group as the vast majority of the country.