The Arbiter is the one who lead the attack on Reach, making him responsible for the deaths of nearly everyone the Chief knew, including 30 Spartan IIs. As for the word friend being used, my personal headcannon is that the term "friend" can apply to brothers in arms. Even though the two hardly interacted with each other, they did fight alongside each other. Given the Elites' martial values, and the Arbiter's personal opinion of the Chief being that he is an honorable warrior, this may explain why he uses the word "friend," just not in the way we use it.