It's not pride, it's more of a rage.
Professor Snape, in Harry's mind, killed quite possibly the closest thing to a grandfather he had ever had - Professor Dumbledore. Not only that, but he was also partially responsible for the death of Sirius Black, the closest thing to a father he had ever known. To use the book would be to use the weapons of a killer, of a murderer.
Harry is a very revenge-oriented hero. You have to do something to tick him off so badly he wants your head at his feet. We all know he's after Voldemort's cold blood and Peter Pettigrew's, for obvious reasons. It took a strong willpower not to kill Peter at the Whomping Willow, and the only reason he probably did it in the first place would be to keep his father's friends from becoming murders, and he felt that he deserved the eternal torture of Azkaban more than death.
So, quite obviously, he would very reluctantly dig through the books of enemies for information, considering everything associated with the Death Eaters to be evil, dispicable, and murderous.
As for Unforgivables, I can see Harry using them on his most hated enemies. Most of the time he feels something called righteous anger, anger that flashes just after the untimely death of a loved one. But, I could see Harry wanting Voldemort and Professor Snape to feel his wrath.