In the flashback scene in Breaking Bad, where Gustavo comes to Don Eladio's mansion to offer business with his partner, why did Hector kill the young chemist?
Hector killed Max on Don Eladio's (non vocal) orders, because he felt insulted. Gus and Max, the Don felt, had manipulated him, through his minons, into having the meeting. By supposedly selling drugs, in his territory, to his men. While Gus and Max may really have gave it away instead of selling it, it doesn't matter to someone like the Don. And by going this way, had the Don refused the meeting, his lackeys would have started to get second thoughts about the Don.
From S4E08 "Hermanos", self-translated:
Why should I negotiate with someone that doesn't respect me?
Who insults me by dealing under my nose without my permission?
Who manipulates me into a meeting...
...in front of my own men?
Essentially, he killed Max because killing any competitors that are muscling in on your territory is standard operating procedure, as is insulting (imagined or otherwise) a mafioso. Can't let these punks disrespect the Don.
He didn't kill Gus because of connections that he may have had/who he was in Chile, which was never disclosed. Had the Don wanted to do business, Hector would not have killed Max, without permission. Otherwise Hector would have been killed.
Basically he doesn't kill him because of his distribution network. Mike says it later in the episode because once again, Gus is not murdered when he walks into the gunfire at the pollos warehouse. Jesse says “so what were all free game, is Gus gonna do anything about it?” It has nothing to do with Gus past like everyone is saying. They literally say it in the episode :)