Hmm, if it turns out to be like Master Chekov's random thought, then it will really make Amuro's character a lot more twisted than it is right now.
I just thought of this. What if Amuro and Akai have sort of a "promise" to each other made earlier in the storyline? Most likely it would be protecting Japan, and thus, protecting Shiho, which I think they're both doing right now (based on Amuro's actions and his relation to Elena). And the reason for Amuro hating Akai is that Akai chose to be part of the FBI rather than the Japanese Secret Police. Maybe Amuro has a deep reason for hating the FBI (killed Shiho's parents, maybe? No one knows how they died, right?) and this could also turn out to be Amuro hating the BO for what they did with Akemi, more the reason to infiltrate it.
Sorry, I just can't help it. I just don't want to see someone as intelligent as Amuro losing shamefully together with the BO when Conan strikes the final blow.