I see this debate everywhere. Some people argue it is not, as they were not lead by the goal of national unity and some kingdoms even sided with the British. Also the fact it was mainly confined to North India. Others argue it is because of the mass insurrection throughout the country. But what exactly is it, if it can be classified as such at all?
The problem with the violence of 1857 is that it had so many meanings, so many in fact that categorising it as one thing or another is almost impossible. Indeed, Chris Bayly, one of the most prominent historians of the mutiny has stated "it was not one, it was many," which in some respects might seem to be an admission of defeat but does help to do justice to the sheer variety of the characterisations of the rebellion. It was constitutional, racial, religious, the first modern war of information and a way of economic dislocation all at the same time.
The first thing I will say is that one thing it certainly was not was a war of independence. The argument that the rebellion represents the first flowering of Indian nationalism and leads directly to the independence of India in 1947 is a long one. Probably the most influential statement of this would be from V.D. Savarkar in his history of the rebellion "the First Indian War of Independence". He argued as early as 1909 that the mutineers of 1857 might be regarded as noble patriots, fighting in a good cause, pro rege and pro patria, for the king and the motherland, for swaraj and swadesh," while drawing on the writings of European nationalists like Mazzini. He chose to see the mutiny as a moment when Indians regardless of race and caste recognised their Indian-ness chose to make common cause to drive the British from India. While that is all well and more recent historians have, in my view wisely, decided to look at the above statement as an ideological statement of the Indian independence movement in 1909 rather than a statement of historical reality.
This then begs the question, where did the impression of the mutiny as a nationalist struggle come from in the beginning. The answer is actually quite simple -- it came from the British themselves. The summation of the British judge at the trial of Badhur Shah (the last Mughal and leader of the rebellion) sums this up. That British rule had created the conditions for European style national consciousness -- "Brahman and Mussulman met here as it were on neutral ground; they have had, in the army, one common brotherhood of profession, the same dress, the same rewards, the same objects to be arrived at by the same means”. This argument was then picked up by people like Sayyid Ahmad Khan (an Islamic Indian philosopher) amongst others.
It would therefore seem that we have reached an impasse. If the rebellion was not India's first nationalist uprising, then what was it? That is a question that any historian could write a very long book on, but I will put forward one interpretation made by Faisal Devji about what the rebellion meant to the troops that participated in it. He argues that the revolt of the sepoys was a legitimist revolt which can be attributed to the feeling that the British had broken their moral obligations as Indian rulers.One way that this can be viewed is through a concept called the “empire of Distinctions.” Whereby the just ruler was meant to preserve and contain the distinctions within a deeply heterogeneous but just society. The soldiers believed that the British were trying to impose cultural and religious homogeneity on them. One thing that particularly drew their ire was the aggressive Christian preaching – something that Charles Grant (a missionary) characterised as “the introduction of light,”to darkened Asiatic despotism. This, was received especially poorly by the soldiers, with one officer commenting that his troops believed that they would “be compelled to eat the same food… that they would likewise be compelled to embrace one faith.” Such a status which the soldiers viewed as being little different from slavery and at least partly explains the position of Bahadur Shah at the head of the revolt, as an exemplar of a religiously tolerant and therefore legitimate constitutional ruler. Therefore, the decision to revolt was based on the idea that they would suffer for each other even though they had no intention of sharing religious or cultural practices. An example of this can be seen in the probably apocryphal story about the greased gun cartridges, which, it could be argued, only exists so as to establish an equivalence and commonality between the Hindus and Muslims.
The final bit that I will discuss here is economic dislocation. British rule from men like James Mill (the father of J.S. Mill was predicated on improvement) and a large part of this assumed that if British conditions were introduced then the Indians would begin to behave more like the British -- i.e. rationally. One of the main ways they did this was through the introduction of British style single title to land. This often had interesting consequences for the Zamindar class in general. For instance when proprietary title was introduced in Bengal it paved the way for many Zamindar Rajputs to be unable to charge rents as they had before. The problem with this is that they did not have enough land themselves to live on comfortably, and if they began to farm they would sink in caste status. As such the rajput class of north India became increasingly dependent on remittances from their sons in the army, but even then this source of income was threatened by the introduction of Sikhs into the army after the annexation of Punjab in 1842. While this community was relatively small in number they are disproportionately important because they were the local magnates in their communities. They provided the organisational know how to make the rebellion self sustaining while at the same time providing a link to their sons who were involved in the Dehli mutiny. Now these are just two isolated but linked case studies, but there are many more out there, and an illustration of how the violence of 1857 defies categorisation.
I recently wrote a multi part answer on 1857, it's historiography and the different interpretations
Edit: The very short takeaway would be that the rebellion of 1857 was a complex war that engulfed different parts of South Asia, and so can't be redused to only one interpretation. And that most later interpretations of the event reflect interests of the groups that put them forward : With e.g. the "insurrection" narrative tied to British colonial views, and the "war of independence" one to certain strands of Indian nationalism going back to the early 20th century.