Well firstly I have to make the obvious caveat that it is very difficult to say why a group of people didn’t want to do something. With that said, there are a few observations we can make.
The first, and probably most crucial, point is that the “Irish Confederation” was not a unified group by any stretch of the imagination. It contained within it a wide range of political actors with their own motives and agendas. It included members of the traditional native Irish elite, but also members of the group known as the Old English; descendents of the original medieval settlers. It is important to point out here that the term ‘Catholic’ referred both to the native Irish and Old English communities. Between the two groups there had also been extensive intermarriage throughout the centuries too, seeing it has a hard distinction is quite misleading. The name they used for themselves was not the ‘Irish Confederation’, but rather the ‘Confederate Catholics of Ireland’. Their motto was Pro Deo, pro rege, pro patria unanimis (“For God, King and Country, Ireland is United”) and this is fairly representative their general outlook.
As a consequence of the Ulster Plantation the native Irish had become increasingly marginalised within their own country at the expense of the new settlers. Of course, there were longer term political developments affecting this too. However, this marginalisation equally applied to the Old English who had found themselves losing political influence at the expense of Protestant newcomers (generally referred to as the New English within the historiography).
Over the course of the 17th century the shared religious ties between the native Irish and Old English had begun to take on a greater importance - something I discuss more in this answer. A shared Irish Catholic identity was beginning to take shape, but the thought of political independence in a ‘capital n’ Nationalist sense, was simply not a feature of their political outlook. It might be no surprise that the Old English historically had tended to emphasise their loyalty to the English Crown, but we actually see this frequently evidenced amongst the native Irish too.
Now this isn’t to say that there was no ‘anti-colonial’ feeling amongst the native Irish, nor that they simply accepted wholesale their domination at the hands of the English. Certainly there is evidence within Gaelic bardic poetry of anti-English sentiment and of a broad national feeling. Likewise it was attempts to increase English control in Ireland that had immediately precipitated the rebellion. They didn’t rebel for no reason. However, it isn’t as simple as viewing the rebellion as a kind of proto-Nationalist rebellion. By the 17th century the English presence in Ireland dated back more than four centuries and so it is natural that politics should largely be understood in relation to the English (by now British) Crown. Expressions of political power were largely defined in relation to this English hegemony.Indeed, the Confederate oath of association contained the phrase:
‘I further swear that I will bear faith and allegiance to our sovereign lord King Charles…and that I will defend him…as far as I may, with my life, power and estate’.
Throughout the war Gaelic poets lauded Charles I as ‘their rightful king’, and saw themselves as ‘Charles’s people’. In every public statement the confederates upheld their loyalty to the king: they were 'His Majesty's loyal subjects'. There was a smaller, radical minority who were prepared to totally reject England and the King’s authority over Ireland, contemplating Ireland as an independent ‘free state’ headed by a native ruler. There were some hints towards foreign support - with one foreign monarchy being substituted for another - but there is no evidence that this was ever a realistic possibility.
As Toby Barnard has noted, total independence for Ireland was more of a ‘rhetorical extravagance than a practicable policy’. To the majority of Confederates there was nothing inconsistent in being both a royalist and a good Irishman.
At the onset of the rebellion in October 1641, Sir Phelim O’Neill had issued a proclamation in which he affirmed this loyalty to the King. In fact the Irish rebels even claimed they had a commission sent from the king himself, authorising them to take up arms. This was certainly a forgery and a political ruse, but that they felt it necessary to do so does tell us something of the political context of the time. O’Neill stated that the rebels "in no way" intended harm to either "the English or Scottish nation", but that they sought "only for the defence and liberty of ourselves and the natives of the Irish nation." As I have noted this ‘Irish nation’ is not the same nation conceived by modern republicans. It is not an independent Irish Republic but an Irish nation, headed by the English King, in which Irish Catholics of both Gaelic and Old English extraction would be free to exercise their faith, and indeed in which they would hold considerable political and economic power.
Of course we shouldn’t accept such public declarations entirely at face-value. There were other motives for those who took up arms, especially as the rebellion spiralled out of the hands of those who had planned it (men of high social standing - landowners, lawyers and clergy), and into ‘the rascal multitude’ who executed it. There is significant evidence at a local level that, although religion was one important feature, social and economic resentment also played a critical role in leading to violence, along with a more general revulsion against colonial society. Nevertheless, if we analyse the leadership who, after all, were the ones doing the negotiating then we are dealing with a different array of motivations, and of men of a different social class.
As noted, the leadership of the Confederacy can be considered a broad coalition of Irish Catholics (both ‘Old English’ and ‘Native Irish’, and indeed even a few ‘New English’). These were generally men of high social standing and wealth. They were united by a shared a Catholic identity and resentment against the trends within English policy, but the specific grievances and sources of resentment could differ significantly.
For instance, some within the confederation wished to overthrow the Ulster Plantation settlement entirely, while others had actually benefited significantly from it; unlike landowners in other parts of the country, those within the English Pale particularly resented their exclusion from places of 'honour, profit and trust' (a phrase they would use often) which, as one contemporary put it, 'they repined so much to want' and which their ancestors had been accustomed to receive. There were of course historical divisions on the basis of provincial divisions and traditional family feuds too, not to mention personal rivalries and antipathies.
As war continued the confederation became split along two lines - those who favoured a peace settlement with royalist forces (represented by the Marquis of Ormond), and a second group centred around the Papal Nuncio Rinuccini, who stuck to a much harder line, rejecting the terms offered by the royalists on the basis that they were not extensive enough in their concession to the catholic faith. All of this is to say that there was not quite one single-minded “Irish Confederation” which might intend one particular thing. In its composition and its aims it reflected a broad spectrum of the Catholic elite in Ireland.
The one thing that had united this Irish elite in the first place was not a single political goal like independence. Rather the common factor uniting all the Confederates was the recognition of their right to practise the Catholic religion, and indeed all took the oath to uphold their liberty of conscience. In addition, in every public statement the Confederates upheld their loyalty to the king: they were 'His Majesty's loyal subjects', and allegiance to the king was enshrined in their oath of association as noted previously.
Finally, a theme which appears in all the negotiations of the Confederates was a determination to secure the independence of the Irish parliament (ie. themselves) - which would function properly as the legislature of the kingdom and which would have greater freedom to initiate bills without prior reference to England as required by Poynings Law of 1494. This wasn't the creation of an independent Ireland, but rather the establishment in Ireland of the machinery of government which would enable it to properly function as a separate nation under the crown of England. In other words what was sought was a form of political devolution within the Stuart Realm, a settlement which would enable them to exercise the Catholic faith and to hold a greater role in the governance of the Kingdom of Ireland.