Why did he kill his bodyguard

People have various opinions on the matter.

To me, I think he killed him because he knew the bodyguard would keep him safe...and he didn't want to be safe. He wanted to die.

Or at least...until the end when he realized he really wanted to live.

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http://i39.tinypic.com/5yd85u.gif

I thought it was because the body guard failed by letting him get pie'd in the face.

My opinion is that he was a selfish scumbag who had everything, and didn't see the lives of others as material or important. So the next step for such a person is to take what even the most wealthy and powerful are not supposed to take in our society, the life of another. His bodyguard trusted him implicitly and gave him a convenient opportunity, that's it.

What a lovely way to burn...

He wouldn't let him get the haircut. Which a) was ruining his plans and b) was none of his business to do. He was the employee telling his boss what he could and couldn't do. So he killed him to get the haircut and because he was pissed.

A bit about the bodyguard from the press kit:
Eric Packer is protected by seen and unseen forces. Kevin Durand plays Torval, Eric’s head of security. At 6’6” he is an intimidating presence, and his character is armed and dangerous. Torval is constantly warning Eric away from his journey, especially as he receives information about “credible threats.” But Eric ignores the warnings and subverts his own security.

Durand sees his character “as a frustrated, ex-Military, father-figure to Eric.” He likens Eric to “his teenage son; I can try to guide him in the right direction, but he will ultimately do what he wants.” Torval’s assistants are Kendra (Patricia McKenzie) and Danko (Zeljko Kecojevic), whose intense encounters with Eric function to further reveal his emotional emptiness.
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We'll never know exactly why since it's never revealed. It seemed that he murdered him for the same reason that kings, mob bosses and dictators murder their servants, annoyance or in a fit of frustration, like swatting a mosquito. Packer is totally insane by the end of the film. (Was the name Packer inspired by real-life Australian mogul Kerry Packer?)

My interpretation is that it was part of the downward spiral, which he was actively pursuing. If he'd fired the bodyguard, or just dismissed him, there would have been no real consequence. But, once he shot the bodyguard, that's when he went past the point of no return. Even if he had turned away at the end, he can no longer return to life as normal. Which is what his wife was offering him.