You certainly have to put yourselves in his shoes. Something to consider, is that Lincoln, like arguably any other leader in history, doesn't want to be known as the president who allowed a secession to succeed.

Interestingly, you are correct in your assessment of Lincoln, in the sense that he didn't have a huge moral stake in the slavery issue, but rather a duty to preserve the union. Here's a quote that sums this succintly:

"A house divided against itself cannot stand. I believe this government cannot endure permanently half slave and half free. I do not expect the Union to be dissolved; I do not expect the house to fall; but I do expect that it will cease to be divided. It will become all the one thing or all the other. Either the opponents of slavery will arrest the further spread of it and place it where the public mind shall rest in the belief that it is in course of ultimate extinction, or its advocates will push it forward until it shall become alike lawful in all the states, old as well as new, north as well as south"

As you can see, he had a tremendous vow to preserve the union, but not to necessarily cause the extinction of slavery.

Something else to consider, is the fact that the North did indeed have a huge advantage over the South, and were fairly confident of an eventual victory. Certainly the military genius of Lee prolonged the inevitable, but a war of attrition was easily won by the North's economic superiority.