As Monk has argued before combining the birthdays of the two greatest leaders of the American Republic into a vapid "Presidents' Day" is a disservice to the gentleman from Virginia and the gentleman from Illinois.
Why Lincoln over Washington? It's not an easy decision but Lincoln successfully prosecuted the most difficult and horrific war in our history where every casualty was an American. In doing so, he preserved the Union.
The importance of that articulated in the last sentence of his greatest speech:
It is rather for us to be here dedicated to the great task remaining before us—that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion—that we here highly resolve that these dead shall not have died in vain—that this nation, under God, shall have a new birth of freedom—and that government of the people, by the people, for the people, shall not perish from the earth.