Title.
Your question presupposes that Washington's government was considered tyrannical, does it not? Washington - and other members of the government at the time - clearly felt as if the Federal government was acting well within its legal authority, not only to levy the tax, but also to suppress the rebellion. However, Washington's actions during the rebellion also show that he was extremely careful about his actions, and how his actions would be viewed by the wider populace, as I will show.
First, I'm going to address some misconceptions - or, at least, specific elements of the amendment that get emphasized over others - about the second amendment, and then I'll describe the ways in which Washington put together a coalition of federal and state governments that worked together to end the rebellion.
The Second Amendment: Context
Some of the roots of the second amendment were found in an earlier conflict, Shays's Rebellion. In 1786, men in western Massachusetts, some of whom faced foreclosure of their farms and homes after a tax increase, mustered together in local militias and posses, blockading local courts and preventing circuit judges from passing decisions in property courts. Calling themselves "Regulators," as they increased in size they increased in organization and discipline, keeping muster rolls, conducting drills, and organizing themselves into numbered regiments. Many of these men were veterans of the War for Independence, and apart from lacking legal sanction, the Regulators were, in essence, a militia organized in exactly the spirit of republican political ideals. I describe these in greater details in this earlier answer.
When the Massachusetts governor called up the sanctioned militia, the problem was further compounded when many of those mustered broke ranks and joined the rebels, in one case 800 men out of 1,000 deserted to the Regulators.
The rebellion was eventually ended after a number of brief skirmishes, and the mustering of out-of-state militias were brought into Massachusetts. Though it accomplished little, fears among the country's elected officials meant that more attention than expected was given to the question of the militia's legality during the constitutional convention in 1789, which eventually resulted in the second amendment.
Though I expect most people are familiar with it, I'll quote the amendment in full:
A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
All in all, not much to go on. But even in the shadow of the Shaysite rebellion, the fact that enough of the representatives felt that securing the legal ability of the citizenry to organize in arms was a major accomplishment; it was, after all, a militia army that had faced down the rebels.
Part of the necessity in pinning down the right to form a militia was the "necessary to the security of a free State," a portion of the amendment that often goes unquoted. Freedom didn't just mean safety for the country against foreign attackers, but safety of the citizen against the government; a government free to raise and employ a standing army to enforce illegitimate laws or to secure the power of a haughty few elites was a fear entrenched in English legal custom and political philosophy since before the Glorious Revolution in 1688. The formation and legal right of militia service was meant not only to form in times of crisis, but also, by simply existing, was meant to impede the government's power to pass or enforce illegal laws or to collect power indifferent to the desires of the people.
If it was only the words of the second amendment to go on, though, this is still incredibly vague and difficult to parse. So much of the wording was based in a cultural context that changed almost immediately, and from the perspective of 2019, this statement is confusing, grammatically complicated, and frustratingly non-specific. Later acts, however, clarified its meaning somewhat. In 1792, congress enacted two Militia Acts: the first to establish the legal framework in which the president was authorized to embody the militia, and the second to set down the framework in which this militia was organized. The first act gave the president the authority to call out the militia "whenever the United States shall be invaded, or be in imminent danger of invasion from any foreign nation or Indian tribe," and further, "... and in case of an insurrection in any state, against the government thereof... to call forth such number of the militia of any other state or states... to suppress such insurrection."
Resistance to foreign invasion and suppression of insurrection were the two primary aspects of the legal embodiment of militia, according to this act. And it's this act which is in place when the Whiskey Rebellion gets started.
The Whiskey Rebellion
Although adding greatly to the detail and the process by which the government could call out the militia, the 1792 acts were still unclear with respect to what exactly constituted an "insurrection." When the rebels embody, organize, drill, and fight within the exact ideological framework of the force expected to put it down, where is the line drawn between legitimate and illegitimate?
However, it was clearly defined that the president had the legal authority to call the militia from neighboring states to act against the rebels, if necessary.
The Whiskey Rebellion was partly prompted by Alexander Hamilton's financial plan, which sought (in part) to tax the sales of whiskey. It was part of a broad plan with a great number of moving parts and goals, but this portion of the plan was met with great derision, perceived as an attack on the livelihood of farmers, and an effort by Washington to strip away the rights and income of the people in order to entrench his own power.
The rebels were popular at first muster, and only looked even more popular in the first months of the crisis. But even in the higher echelons of state and federal power, there were deep ideological divisions. Federalists, those who had supported the constitution in 1789, were now a party devoted to shoring up and defending the power of the federal government as an arbitrator, but still subservient to checks and balances from individuals and states. The old Antifederalists, on the other hand, had formed into a new party, the Democratic-Republicans, and sought to curtail the power of the federal government, and support the power of states to govern themselves free of federal interference (this is vastly simplifying a complicated process and political playing field, but bear with me).
Federalists perceived the Whiskey Rebels as malefactors deliberately agitated by radical antifederalists to roll back the constitution and strip it of its power, and thereby plunge the nation into anarchy. The Democratic-Republicans, however, saw any effort to suppress the rebellion as an engineered crisis aimed at increasing federal power and stripping it away from the states.
Against this backdrop, Pennsylvania governor Thomas Mifflin, refused to call out his state's militia to deal with the rebels. Deeply suspicious of using force to solve the crisis, Mifflin pointed to widespread refusal among Pennsylvania citizens to muster against the rebels, and the unpopularity among the citizenry to the new tax scheme. Mifflin was also hostile to bringing out-of-state troops to quell the rebellion, as well.
The argument continued even in the president's cabinet. Another Pennsylvanian, Thomas McKean, the Chief Justice of Pennsylvania, summarized the feelings of many as the rebellion spread: "the employment of military force, at this period, would be as bad as anything the Rioters have done - equally unconstitutional and illegal."
Washington spent several months seeking a peaceful solution, even as rioting spilled over from Pennsylvania into Maryland. He delayed musters and rendezvous, conscious all the while of what a speedy military suppression would say to the country at large.
It was only until September that Washington felt that the rebels had squandered widespread public symapthy, and that military force was justified in putting down the rebellion. By then, he had bipartisan support among his cabinet and support of state governments, and the public was firmly in support of ending the insurrection. It was only then that the militia marched against the rioters. And in the end, the rebels scattered, their ringleaders were captured, and the rebellion fizzled out with barely a shot fired.
Even then, complaints surfaced about the conduct of the out-of-state militias, who had allegedly looted, vandalized, and terrorized locals along their route of march, even more firmly entrenching the idea that the only valid embodiment of military force should come from local militias instead of an aloof force of strangers.
In the end, Washington hadn't felt as if military force was justified, until he had garnered public and political sympathy for the cause. He spent months looking for a peaceful solution and when that was exhausted, only then did he muster troops for a military solution. This had gone against several members of his own cabinet, including Hamilton himself, who had proposed mustering a force of 12,000 regular soldiers (with himself in command, naturally) to march on the rebels.
The first and second Militia Acts of 1792 are linked above.
For further reading, I would suggest Richard H Kohn, Eagle and Sword, Lawrence Cress, Citizens In Arms, and Saul Cornell, A Well-Regulated Militia
Because he didn't think that his government was tyrannical. Obviously that's an over-simplification, but clearly Washington (like, I imagine, basically every executive who's ever been rebelled against) saw his authority as legitimate. It had been vested in him by electors who represented the people of the states as spelled out in the Constitution. Washington's views on rebellion and an armed citizenry were fairly complex. He, along with basically everyone at the time, saw the right to own a gun as an essential element of an expanding society. For those living on the frontier, a gun was an essential tool, providing protection against attack by Native Americans, defense against dangerous animals, and gathering food by hunting. The modern idea of 'gun control' would have been completely alien to early Americans.
Now, the right to own a gun does not mean that you have the right to do whatever you want with it. Much has been written about the 2nd amendment and its intent. However, one thing that it absolutely does not provide is a "right to revolution." When Washington suppressed the Whiskey Rebellion, he did so at the head of an army of 13,000 militiamen, provided by Virginia, Maryland, New Jersey, & Pennsylvania. These militias ("well regulated" as mentioned in the 2nd amendment) had been created by the two militia acts of 1792. The first militia act gave the president the power to call up the militia in event of "invasion from any foreign nation or Indian tribe" or "in case of an insurrection in any state."^(1) The second act details the structure of militia companies, who is a member, and who they report to. All militias reported up the chain to the state legislature, who (as per Militia Act 1) fell under the authority of the executive.^(2) As a result, the militias created by the acts were fundamentally tools of state (and executive) power. They were explicitly empowered to act against both external invaders and internal rebels ("enemies foreign and domestic."). So, rather than being a bulwark against tyranny, the 2nd amendment (along with the militia acts) actually provided a means by which a government could suppress internal rebellions.
Washington in particular was very much in favor of centralized military power, both during the revolutionary war and afterward. His experience during the revolution led him to be skeptical of militias generally. He saw them as unprofessional, undisciplined, and likely to desert. Much of his war-time correspondence with Congress was related to his desire for a national army.^(4) Those letters included frequent criticisms of the unprofessional behavior of the militiamen under his command.
The idea of a 'right' to overthrow a tyrannical government is inherently nonsensical. Regardless of where you believe rights originate (nature, God, rational thought), they do not exist in a vacuum, they need to be enforced by some kind of legal / judicial system. For example, it doesn't matter if you have a "right" to own property if there is not some kind of enforcement mechanism to defend that right (police, courts, etc). Absent enforcement, your neighbor could just walk onto your land and take your stuff. As the Declaration of Independence notes: "to secure these rights, Governments are instituted among Men." In this framework, a "right to revolution" is self-contradictory. A government cannot recognize a right to ignore its own authority. So, while the 2nd Amendment may create the circumstances that allow for armed resistance to tyranny, it does not permit actually doing so. You have the right to own a gun, but once you take that gun and point it at the government, you are breaking the law. There's a reason that Treason is the only crime described in detail in the Constitution.^(5)
Citations:
If taxation was the "cause" of the Whiskey Rebellion, then why did the federal government need these taxes in the first place? What was the declared mission of the federal government which necessitated this taxation?
Was the general population aware of what these taxes were going to be used for? Could they have been seen (by some) as unnecessary, frivolous, wasteful, or otherwise unwarranted? This seems to be the core of the question, that a refusal to pay legislated taxes is unlawful, and enforcement WILL happen.
I sense that this is an enormously complex topic.