The first time Miles meets the Eagle, he's treated to a Look of Doom that does not yet portend doom. But that's only the first time.
The Eagle plays a necessary role at the Creek, namely as the martinet who enforces the rules. He doesn't rule alone, though—a student-run Jury helps him govern the Creek.
There is more to the Eagle than a hawkish eye, though. Yes he gets disgusted by the audacity of the students (or perhaps their inability to get away with their mischief), but that doesn't stop him from feeling real affection for them. Check this scene out:
Alaska crouched down, picked up the cigarette she had thrown away, and started smoking again. The Eagle wheeled around, his sixth sense detecting Insubordination To Authority Figures. Alaska dropped the cigarette and stepped on it. The Eagle shook his head, and even though he must have been crazy mad, I swear to God he smiled.
"He loves me," Alaska told me as we walked back to the dorm circle. "He loves all y'all, too. He just loves the school more. That's the thing. He thinks busting us is good for the school and good for us. It's the eternal struggle, Pudge. The Good versus the Naughty." (99before.14-15)
Alaska's analysis is spot on. Because we only get Miles's fearful perspective of the Eagle, we don't really realize that there might be more to the Eagle as a person than he lets on to students. In addition to the fondness he lets slip out in the above passage, we also see a glimmer of humor here and there:
"Don't ever do anything like that again," he said. "But, Lord, 'subverting the patriarchal paradigm'—it's like she wrote the speech." He smiled and closed the door. (102after.44)
When his sense of humor and appreciation for quality pranks is paired with his true grief at the news of Alaska's death, the Eagle ceases to be the one-dimensional disciplinarian we initially see him as, and becomes a disciplinarian with a heart of gold.