I believe the reason "psychologists have trouble agreeing on the function of this complex emotion." is because our conscience comes from God. If you want to know why you feel guilty you have to look to the Bible.

"Even Gentiles, who do not have God’s written law, show that they know his law when they instinctively obey it, even without having heard it. They demonstrate that God’s law is written in their hearts, for their own conscience and thoughts either accuse them or tell them they are doing right. And this is the message I proclaim—that the day is coming when God, through Christ Jesus, will judge everyone’s secret life." Romans 2:14-16 (NLT)