It very nearly didn't. There had been several rebellions prior to independence, most famously the Inconfidência Mineira, which likely would have seen independent countries. Likewise after independence there were several breakaway attempts, the most successful of which, the Farroupilha Republic, managed to hold together for a decade or so.

So why didn't they succeeded where the Spanish attempts failed.

First and foremost Brazil was ruled as a single united entity. Attempts at making a series of separate colonies failed. Originally Brazil had been divided into a series of capitancy-generals, the majority of which all but immediately failed. A variety of other divisions had been tried but by 1775 everything had been subsumed into the state of Brazil, and Brazil had been elevated to a viceroyalty. This meant that everyone looked to Rio de Janeiro, not Lisbon. While authority ultimately derived from Portugal it was always translated via Rio. This created a "unified" state had existed for a half century before independence. And the crown actually lived in Rio for over a decade. Centralization and consolidation had been a thing for sometime. Baihanos, Pernambucanos, and others though of themselves in local terms, but they also thought of themselves as Brasileros. Men of status looked to Rio for promotion.

The Spanish Empire in contrast was divided into dozens of viceroyalties, audiences, intendencies, governships, capitancy-generals etc. and all of them looked back into Spain. There was no real "center" of the Spanish Empire. Instead there were regional and local centers. Men of status looked either to these local centers or back to Madrid. Plus these were divisions were changed up as needed. Although the four viceroyalties were more or less stable, their borders were regularly adjusted. Central America for example spent time as part of both New Castile/New Spain (Mexico) and as part of New Granada (Columbia). So they never developed strong ties to either Mexico City or Santa Fe de Bogotá.

When the Spanish empire rebelled it did so in a piecemeal fashion. Each rebel faction was tied to their own region. There were men like Bolivar who attempted to create a pan-national identity and movement. But coordination was too difficult. Plus a lot of the groups had very different goals, further impeding unity. Ultimately most broke on existing smaller divisions.

In contrast when Brazil went independent, it was declared by Don Pedro I, the crown prince and regent of The Kingdom of Brazil. He had the backing of the nobility, aristocracy, gentry, and commons. It was a largely a peaceful rebellion; for most people nothing changed. They lived under the same laws and even the same man. By the time the folks in Rio Grandense decided they had enough and wanted local independence, Brazil had had a couple decades as an independent state. And Don Pedro I had an imperial army, making breaking away a much more difficult process.