My understanding is that the Rohingyas are migrants from Bangladesh (with a densely-packed population of over 150m). The label Rohingya itself is fairly recent and it represents anyone who looks like a non-native in that region (because the majority ethnic group there is Rakkhine and they are fairer-skinned than the ones migrated from Bangladesh, who look more like people from India or South Asia). They speak Chittagong, which is a local dialect of Bangladesh as well. But they have been slowly migrating into Myanmar since early 1900s (the borders are porous and the enforcement of legal settlement is non-existent especially for a poor country like Myanmar) and have accrued in numbers over the years. Unfortunately, a few guys from the migrant community raped and murdered a local girl from Rakkhine ethnic group a few years back (I think, it was in 2012). Because of that, the tension between the locals and the migrants rose to an unprecedented level, resulting in people being killed on both sides. But because Rakkhines are the majority, their casualty is significantly lower. The current Myanmar government invited a UN panel, led by former UN chief Kofi Anan, to assess the situation and give recommendations. Their findings and recommendations just came out recently [1] and their report is quite mild and does not mention observation of any violence (or ethnic cleansing) against Rohingyas in the region like some western media usually portrays.
Think about it this way: what if the US's economy is as big/poor as Myanmar and yet over a million people (with very different religious and cultural background) from an overpopulated neighbor (say, Mexico with significantly smaller land area) migrated to the US. In addition to that, the migrants want to be granted citizenship as well as be given an autonomous region to protect themselves from the natives, how would you handle that? Not even a country, as resourceful as the United States, can deal with the migrant issue properly at the moment. So, it is really a tall task for Myanmar government and people living in the country.
Finally, please keep in mind that the NGOs (including the UNGOs) aren't the most trustworthy sources of news. The people from NGO need budgets and donations from parties of interest, and it is sometimes good for them to keep things, at least, exaggerated to make sure the funding keeps flowing in (I interned at Save The Children and World Concern for a total of about 5 months in Myanmar; I also have friends who have worked or are still working in INGOs in Myanmar and they've told me of the conflict of interest that the NGOs usually have in such issues). There are also self-acclaimed "activists" from Myanmar (including some Rohingyas themselves), who give interviews to the western media and cries about the purported sufferings of minorities so that they can claim asylums in other countries (e.g., the United States and the Europe ). I say that because I know a LOT of people from Myanmar in the US (two lives in the house that I currently live; one of them used to work as a logistic person for UN for more than three years and she had worked in Rakkhine on the Rohingya issue) who have already filed for their asylum-ship related to ethnic strifes despite the fact that they came from middle class families and were never persecuted as such is claimed in their asylum applications. But in preparing for their asylum-ship application, they participate in protests and events related to Rohingyas and other minorities to make sure they get the photographic evidence of their participation in the issue.
Long story short, the issue is not as black and white (Rakkhine people bad, Rohingyas oppressed) as you'd read in the news. As most things in life, there are more than one side to the issue.
[1] http://www.reuters.com/article/us-myanmar-rohingya-annan-idU...