Because he saw Inaho fighting Saazbaum, and then watched Seylum tend to Inaho while he was injured in his Kat. Despite them hating each other, Slaine saw that Inaho wasnt a threat to Seylum. He shot him out of jealousy. There was no need to point a gun at Inaho while he was injured and crawling towards Seylum anyways.
All that matters to Seylum, if shes alive, is that Inaho was the dude that saved her multiple times as well as one of the few that were capable of defending the terrans. And Slaine murdered him.
IIRC, Slaine also fired first during their first meet up, when he wouldnt answer Inahos question. So, #FUCKSLAINE
A lot of people have already made very good attempts at explaining Slaine's actions and his frame of mind when he helped Saazbaum, but whatever, let's just agree that was a mistake, and from all indications, Slaine is well aware he made a mistake and the guilt is killing him. Characters are allowed to make mistakes, it humanises them, it doesn't make them terrible.
There was undoubtedly an element of jealousy when Slaine shot Inaho, obviously, but how was that not understandable? Here you have this guy killing himself to get to the girl he loves, making enemies of both side along the way, going through the hell to get to her, and when he finally does, before she can even notice he's there, she's murdered in cold blood. Someone is going to have to pay, and of course Saazbaum gets shot a number of times, and then there is Orange, his known enemy, the one that prevented him from uniting with Asseylum in the first place, and he's trying to get to her, so what does he do?
Inaho might not have been a threat to Asseylum, but neither was Slaine at the time Inaho shot him down so while I'm not sure if Slaine had already made his mind up to kill Inaho when he was crawling to her, he did give him a fair warning, and the last time he gave Inaho a warning, Inaho beat him to the punch and left him for dead, so this time around, Slaine wasn't going to hesitate shooting someone he knew to be his enemy and who he deemed partly responsible for Asseylum's apparent death. Had Inaho not pulled a gun on Slaine, things might have gone differently.
I just think it's funny in a tragic sense that seemingly everyone couple empathise with Slaine throughout the show when he was getting hammered every episode, but the one time he does something, when he is at his lowest point, you unleash this level of vitriol on him.
Is Urobuchi going to be involved in any way with S2? I remember he wrote the first 3 episodes of S1, so wondering if he will write any from S2.
I hope not if that means Inaho x Asselyum. I'm seriously still holding out for Slaine x Asseylum, as unlikely as that is. I don't even care if the dude dies in the end.