Lincoln believed (with good reason) that his Consitutional authority to emancipate slaves was limited to areas under rebel control.
All of the above are the words of Abraham Lincoln...
The public letter to Horace Greeley that you quoted stated Lincoln's position as of the date it was written (July 1862). At that time a large majority of Americans did not want to see the war transformed into a crusade for abolition, but note that Lincoln was still indicating in that letter that he was contemplating some sort of emancipation order.
In order to hold the Union together in 1862, Lincoln needed the support of conservative Republicans and War Democrats as well as Radical Republicans. Lincoln eventually moved very close to the position of the Radical Republicans on abolition and negro suffrage, and in fact it was the speech Lincoln gave in April of 1865 -- wherein he became the first President to advocate negro suffrage -- that so enraged John Wilkes Booth that he assassinated Lincoln.