How to explain philosophical disagreements ? A broad variety of considerations play their part but I am not inclined to put all or even most philosophical disagreements down to differences in intuition as will become clear.
'Intuition' is a term with many shades of meaning. Some at least of these must be noted :
▻ Intuition as knowledge of self-evident truth - and particularly (in Descartes) of truths which are foundational to all knowledge and reasoning. (Regulae, XII.)
▻ Singular and immediate representation of particular objects via the senses (Kant, Critique of Pure Reason, A49, B72).
▻ Belief instantly produced without prior deliberation.
▻ A hunch, a sense, a feeling that things are thus-and-so on recognisedly imcomplete evidence.
My own intuition or hunch is that the kinds of intuition relevant to the question are the third and fourth.
Time now to explore the sources of philosophical disagreements.
Evidence and judgement
Some philosophical disagreements arise from inferior evidential situations (unrecognisedly incomplete evidence) or inferior judgement between the disputants. I am not espousing rampant elitism. But I have known, for example, disputes about whether physical objects are 'really' coloured or whether we merely see them as coloured where one side is simply ignorant of the physics and neurophysiology of vision. The dispute is philosophical to the extent that it affects the question whether we should include coloured objects in our ontology; and it connects with philosophical issues over primary and secondary qualities which date from Locke (Essay concerning Human Understanding, 1690, II.viii.8) and earlier. There can also be and are inferiorities of judgement as when someone cannot see that 'If p then q; q : therefore p' is a fallacious argument (here the fallacy is that of affirming the consequent).
Failure to suspend judgement
There are cases where philosophers who are epistemic peers - all as clever, well-informed, &c. as the others - disagree. I should say that modal realism about possible worlds in ontology and the issues between internalism and externalism in epistemology are examples of this. The right response to this situation, since there are strong arguments on both sides but no decisive arguments on either side, is suspension of judgement. But some philosophers are unable or unwilling to see that the disagreement of their epistemic peers is evidence of which they should take account, and back their own judgement dogmatically and, as I should say, irrationally. (If you reject my examples, you can find others that fit the case.) I take 'judgement' here to be more than a belief instantly produced without prior deliberation or a hunch.
Failure of full analysis
When there are entrenched disputes that seemingly resist resolution, it is sometimes the case that the disputants are at cross purposes. In the famous dispute in the 1950s between Philippa Foot's 'naturalism' and R.M. Hare's prescriptivism in ethics, it eventually became clear that they simply had different views of the nature of morality. Foot tied moral judgements to considerations of benefit and harm; Hare ignored content (at least in his earlier work) and counted anything as a moral judgement or principle as long as (a) you were prepared and motivated to act on it and (b) you were willing for others to act on it in the same circumstances as your own. (A bit simplified.) Foot and Hare did disagree but largely they were at cross purposes about the nature of morality : each stipulated different criteria for a judgement or principle to count as 'moral'. In this kind of disagreement more is likely to be invovled than beliefs instantly produced without prior deliberation or hunches.
Situational ethical disagreements
Ethical disagreements can arise from other sources than cross purposes. Nearly always in a moral dispute factual considerations are involved. I do not need to enter here into the viability of the fact/ value distinction or the proscription on deriving an 'ought' from an 'is'. Simply consider the question whether the Second Gulf War (2003) was a just war. At least part of the issue turned on whether in fact Saddam Hussein possessed weapons of mass destruction. The justness or otherwise of the war involved many other considerations but this was at least one consideration, whatever weight one attaches to it. If Saddam did not have WMD then this part of the moral case for the war - this ground of entitlement to call it a just war - was eliminated. Here was factual disagreement here, which informed (or misinformed) and coloured the just war argument. There appears no role for intuition here, simply a disagreement over the reliability of information.
A place for intuition at last ! There are two possible solutions to the Newcomb Problem, a paradox in decision theory presented by Robert Nozick in 1969 : the one-box solution and the two-box solution. There are strong intuitive arguments for both solutions; and decision theorists divide accordingly. There has been a slight shift towards favouring the two-box solution. But there is, as far as I know, no appeal beyond intuition (in the sense of hunch or feeling for what's correct).
There is a place for differences of intuition in explaining philosophical disagreements but several other factors can also produce disagreement.
R. Nozick, 'Newcomb's Problem and Two Principles of Rational Choice', reprinted in Socratic Puzzles, Cambridge, Mass : Harvard University Press, 1997, 44-73.
Richard Feldman & Ted. A. Warfield, ed., Disagreement, Oxford : OUP, 2010.