The LORD is my light and my salvation, whom shall I fear? These bold words introduce this psalm. 
27:1-6 sound more like a psalm of confidence or praise 
27:7-14 sound more like an individual lament as David pours out his problems to God
Some have suggested that these were originally two different psalms. However, a common vocabulary ties the portions of this psalm together: "God of my salvation" vs. 1, 9; "adversaries" or "foes" in vs. 2, 12; "heart" in vs. 3, 8, 14; "seek" in . 4, 8, 9. These are some of the common links in the psalm. 

Two verses that stand out to me are verses 4, 10.
In vs. 4 he desires to be in the house of the LORD more than he desires anything else.
In vs. 10 he asserts that the LORD will not forsake him. The LORD is more reliable than the most certain cases of human love. 
So he affirms his desire not to forsake God on the basis of his knowledge that God will not forsake him.