Someone's "last words" are incredibly important
They give us a look into what that person cared about and wanted to represent. They usually carry more weight than anything that person had said before that point.

How we got to this point
Jesus has already been betrayed, convicted, beaten, and is now hanging on the Cross - just to provide some context.

Why would Jesus say this... making it sound like God abandoned Him?
Even though this psalm is technically a Psalm of Lament, it doesn't end that way.

Jesus articulated the pain He was experiencing and His victory in one sentence
By quoting this Psalm, Jesus is demonstrating His humanness and divinity all at once.