In his first cutscene he is very much believable. He reminds the Chief that there is a whole boatload of people aboard Infinity that are his, Del Rio's, responsibility to protect. He insults the scientists, and looks down on Master Chief's heroic inclinations. I have worked with people who behave very much like him and know enough military personnel to know that this kind of behavior is common and expected.
What I'm saying is, is that it is very believable. More than this, though the player might not get the warm fuzzies while meeting him, they will realize that what he is saying does have a grain of truth to it. The value of living to fight another day is, in fact, underestimated by Chief.

We then see him deciding not to send in LAND recon before acting. He already has recon of what the mission objective will be, a network of particle cannons. He then explains that he believes there is no time to send in "force recon" to get better knowledge of what is on the ground. This is believable. While it is always preferable to go in with lots of recon, sometimes it isn't possible. Here, Del Rio thinks it isn't possible and Chief thinks that it is possible.
But remember, Chief has just tried to undermine Del Rio's plan, suggesting that they stay on Reqium longer. So when Chief suggests taking even more time he is a little bugged but yet another suggestion of the Chief's.

Lastly we see Del Rio being confronted once again with Chief trying to pursuade him to stay on Reqium and put more lives in danger. The Chief now tell him about a "vision" he had from an old imprint of a real forerunner. You will understand if he is skeptical.

Imagine if an old legend (frozen for years) suddenly appears on your ship, starts trying to tell you that you are doing a bad job of being a captain, and then tells you that he has been chatting with long dead Forerunners and that they "unlocked" some kind of power within him. Now imagine that you watch his AI (which you know is going rampant) flip out and literally explode break all sorts of shit on your bridge. She is clearly unstable and needs to be removed from your system.

After all of that, yeah i will him a little slack for being pissed. Also, I still think he is kind of a douche and should have listened to the Chief, but at least I can see it from his side.

If this was real life, I doubt the military would have immediately taken the ship away from him. Honestly, that was bad writing.