I haven't been able to find anything written by Abraham Lincoln himself explicitly explaining his reasons for declining the position of Governor of the Territory of Oregon in September 1849.
The surviving correspondence might suggest several reasons, and in particular at least one contemporary seems to say that he may have felt embarrassed to take such a post while friends whom he had recommended for office were rejected.
Lincoln's first (and only) term in Congress ended on 4 March 1849. Shortly after the end of his term, Lincoln had recommended Cyrus Edwards for the position of Commissioner of the Land Office, noting that if Edwards was not acceptable to the Administration he would accept the office himself. In the event, Justin Butterfield was appointed (despite the fact that Lincoln had the support of most of his party) [Arnold, 2008, p81].
His experiences with the Commissionership, and with other matters of patronage at that time, do seem to have given Lincoln a jaundiced view of government. This may also have been a factor in his decision to decline the offer of the governorship. In a letter to John Addison the following year (9 August 1850), Lincoln wrote:
... The substance of the matter you speak of, in detail, has long been
known to me; and I have supposed, if I would, I could make it entirely
plain to the world. But my high regard for some of the members of the
late cabinet; my great devotion to Gen: Taylor personally; and, above
all, my fidelity to the great Whig cause, have induced me to be
silent; and this especially, as I have felt, and do feel, entirely
independent of the government, and therefore above the power of it's
If he felt that way in September of the previous year, that would go a long way to explain the reasons for his refusal.
What we do know is that Lincoln wrote to Secretary of State John M Clayton on 21 August 1849, advising that he had received a letter notifying him of his appointment as "Secretary of the Teritory of Oregon" [sic] and accompanied by a Commission. He said:
I respectfully decline the office. I shall be greatly obliged if the
place be offered to Simeon Francis, of this place [Springfield].
On 23 September, he wrote to Thomas Ewing, Secretary to the Treasury, from Tremont Illinois to advise him that:
Your dispatch of the 20th announcing my appointment as Governor of
Oregon is just received, having reached Springfield in my absence, and
been forwarded to me here by mail. I have just written a friend at
Springfield to answer you by telegraph that I decline the appointment,
which I suppose will reach you long before this will. May I request
you to express my gratitude to the President for these repeated
evidences of his kindness and confidence?
The telegram, sent on 27 September, reads simply:
I respectfully decline Governorship of Oregon; I am still anxious
that, Simeon Frances shall be secretary of that Territory. A. LINCOLN
Lincoln's brother-in-law also notified the chairman of the Illinois State Whig Executive Committee, A.G. Henry, about Lincoln's decision. Henryy wrote to Secretary Ewing on 24 September 1849. He said that Lincoln:
has declined the office of Governor of Oregon and for reasons I
presume entirely personal to himself and certain friends whose
claims he early pressed upon Genl. Taylor for appointment to office. I
know Mr. Lincoln is disposed to yield the administration his most
cordial support notwithstanding his refusal to take office for
himself, so long as his friends are unprovided for.
[Miller, 2010, p240]
This does seem to support the idea that Lincoln was embarrassed, or at least unwilling, to take a post in the patronage of government while friends whom he had recommended for office were rejected.
The subject of Lincoln and the Governorship of Oregon was explored in a paper by Paul I. Miller, presented in The Mississippi Valley Historical Review in December 1936.
Arnold, Isaac N: The Life of Abraham Lincoln, Digital Scanning Inc, 2008
Miller, Richard Lawrence: Lincoln and His World: Volume 3, The Rise to National Prominence, 1843–1853, McFarland, 2010