The question pretty much says it all. The American history i was taught (I'm American, by the way), teaches exclusively the former, but it seems unlikely that there weren't at least a couple other reasons that played a role to some degree.
It wasn't exclusively either, but a mixture of them and other motivations. Washington retired three times. First from his military commission in 1759 and, while he was still an elected delegate to the House of Burgesses, he was intent to then be a full time farmer. That lasted about 16 years, until 1776, when he traded his farming life and spot in the Burgesses for a role as General of the newly commissioned army. In 1783 he again intended to retire, once more resigning his comission back to the government and going home to farm. A few years later, he was asked - basically begged - to lead the delegation headed to Philly in 1787 to discuss altering the Articles of Confederation in order to address problems with the lack of federal authority in the charter. He would begrudgingly accept, and upon that Congress assembling, he was elected as their President. Instead of altering the A.O.C., the Virginia Plan was introduced and they began to discuss replacing the charter outright, which ultimately is what happened with their signing of the Constitution in Sept of that same year. Following that, Washington was elected President and wouldn't deny the honor and responsibility of establishing our newly chartered executive branch. He did a [great job] (https://www.reddit.com/r/AskHistorians/comments/gkqd62/people_think_of_george_washington_mostly_known/), too (as I covered in a previous reply).
Then came retirement, again, and it was, again, short lived. He had grown weary of politics and had watched Hamilton and Jefferson create rival factions. He had seen the 1794 crisis with England, partly resolved by the Jay Treaty, but that treaty also caused more turbulance - and factional (or "partisan") divide. On one hand, he was tired. He missed his farm. He longed to be away from the focus of public life. But on the other, he placed great importance on properly establishing our young Republic. Part of that importance, however, was appearing to be a republic and not a monarchy. Jefferson had been labeling some as "monocrats" already, and had left the administration himself (partly to escape Hamilton from frustration, partly to finally retire himself - like Washington's retirements, it didn't take and he was soon VP). Washington promised not to become a powerful monarch and he meant it. His largest concern on the issue was if he were to die in office, which in his 60's wasn't unreasonable to expect, which would have established a precedent of a lifelong presidency, reaffirmed by elections every four years, which was something he did not want to do. According to Mt Vernon historians, it was this desire that fueled his retirement more than any other single reason.
Adams took the position and much stayed the same - the cabinet, for instance, was retained. Washington kept an interest and requested to the Secretary of War that he keep him updated on all developments, particularly as it relates to French relations, as long as he wouldn't be sharing confidential information. But soon we found ourselves on the brink of war, this time with France. After the XYZ affair we were so close, in fact, that Congress approved raising an army - an army that needed a commander. Washington was offered the job and accepted under the condition he only leave Mt Vernon in the event of a French invasion or in the immanence of such an invasion. Adams had agreed to place Hamilton as his second, but changed his mind, infuriating Secretary of State Timothy Pickering (who was so opposed to the Democrat-Republicans he later tried to create a New England Confederacy closely allied with England). Pickering and Washington both wanted Hamilton to get the job, and he ultimately did, but Adams suffered with certain Federalists as a result. Before long, though, Washington was back in Philly and suddenly found himself charged with raising the officers for Virginia, to which he protested he wouldn't know who to pick any better than any other Virginian, having now been so long removed from that theatre of service. He began to really be disinterested in the whole endeavor, and for the first time did not put his every fiber into the task of serving placed upon him.
With Adams slightly tarnished and the Republicans growing in strength, Washington began to support select Federalist politicians and urged them to run for particular offices, something he had avoided since his early days in the Burgesses in the late 1750s. It was Spring of 1799, and Jonathan Trumbull, Jr soon asked Washington to seek a third term in 1800, to which Washington replied;
It would be matter of sore regret to me, if I could believe that a serious thot was turned towards me as his successor; not only as it respects my ardent wishes to pass through the vale of life in retiremt, undisturbed in the remnant of the days I have to sojourn here, unless called upon to defend my Country (which every citizen is bound to do)—but on Public ground also; for although I have abundant cause to be thankful for the good health with whh I am blessed, yet I am not insensible to my declination in other respects. It would be criminal therefore in me, although it should be the wish of my Country men, and I could be elected, to accept an Office under this conviction, which another would discharge with more ability; and this too at a time when I am thoroughly convinced I should not draw a single vote from the Anti-federal side; and of course, should stand upon no stronger ground than any other Federal character well supported; & when I should become a mark for the shafts of envenomed malice, and the basest calumny to fire at; when I should be charged not only with irresolution, but with concealed ambition, which wants only an occasion to blaze out; and, in short, with dotage and imbicility.
All this I grant, ought to be like dust in the balance, when put in compet[it]ion with a great public good, when the accomplishment of it is apparent. But as no problem is better defined in my mind than that principle, not men, is now, and will be, the object of contention; and that I could not obtain a solitary vote from that Party; that any other respectable Federal character would receive the same suffrages that I should; that at my time of life, (verging towards three score & ten) I should expose myself without rendering any essential service to my Country, or answering the end contemplated: Prudence on my part must arrest any attempt at the well meant, but mistaken views of my friends, to introduce me again into the Chair of Government. - G Washington to J Trumbull, July 21 1799
He was saying it wasn't his country and it wasn't him that would be voted for or against, but rather our country and the votes would fall on values of the factions represented, not the individuals themselves. And if that be the case, why does he need to be the one? Surely anyone else representing the same faction would fair equally well, and with his legacy of unparalleled service there was no good reason for him to muddy it by entering the political chaos found at that time. He wanted, at long last, to retire and run his farm. He was rapidly becoming politically unimportant, in his own mind anyway, and it was time for others to lead as he had.
So he did retire, yet again. He wrote two wills in July and he then spent the summer and fall managing his farm and household. He was where he wanted to be. He would ride the estate, taking notes of what needed attention. As winter approached, he made elaborate plans for his estate, planning everything wanted or needing to be done for Mt Vernon over the next three years - from fields and crops to barns and workshops, expansion plans, all of it - and on Dec 10 he drafted a long letter conveying his thoughts and, along with the plans themselves, intended to give them to his overseer, a Scot named James Anderson. On Dec 13 he took such a ride on his farm and drafted another letter to Anderson;
Mr Anderson
I did not know that you were here yesterday morning until I had mounted my horse, otherwise I should have given you what I now send. [Being the letter and plans]
As Mr Rawlins was going to the Union Farm, to lay off the Clover lots, I sent by him the Duplicate for that Farm to his brother—and as I was going to River Farm myself, I carried a copy for that Farm to Dowdal—Both of them have been directed to consider them attentively, & to be prepared to give you their ideas of the mode of arrangeing the Work when they are called upon.
Such a Pen as I saw yesterday at Union Farm, would, if the Cattle were kept in it one Week, destroy the whole of them. They would be infinitely more comfortable in this, or any other weather, in the open fields—Dogue run Farm Pen may be in the same condition—It did not occur to me as I passed through the yard of the Barn to look into it.
I am Your friend &ca
Go: Washington
It was business as usual. That evening, after his ride, he would head directly to supper still wearing his wet clothes, having been caught in a wintery storm on his ride. 20 hours later, our first president gave strict instructions on his last wishes, and when he was satisfied he had been understood, he simply said "Tis well," and with that, on Dec 14 1799, our first president took his last breath.
A fantastic look at Washingtons life is Ron Chernow's excellent biography, Washington: A Life (2010). Another fantastic (and much shorter) read is the [speech] (https://washingtonpapers.org/resources/articles/george-washington-in-retirement/#:~:text=This%2C%20his%20second%20retirement%2C%20lasted,he%20died%20at%20Mount%20Vernon.) given just a few days before the 200th anniversary of his death by William Wright Abbot (Abbot was the editor for The Washington Papers, spending 20 years cataloging and studying the writings of George Washington - at this point his papers have 47 volumes and over 135,000 documents).