I know there's a reason for each trap Jigsaw did, but he claims he's never killed anyone and that it's the victims' own fault if they don't have what it takes to survive, hence the jigsaw symbol he cut from the dead victims that got him his name.
But what about the traps where either the victims' survival is completely out of their hands, or at least one person has to die? Yes, he was trying to teach someone something each time, but doesn't it go against what he claims to believe in? Even if in most of them they technically kill each other, he still put them in a situation where at least one of them had to die, it's just up to them which one/s. (I guess we can just chalk it up to him being demented)
Note: I might have forgotten the official names of some of the traps
The Bathroom Trap - Dr. Gordon has to kill Adam, or else Zep kills his wife and daughter. Leaving their fates in Dr. Gordon's hands, and he has to choose between Adam or Allison and Diana. And Allison and Diana are completely innocent so Jigsaw shouldn't be involving them at all.
The Reverse Beartrap - Amanda has to slice open Donnie's stomach for the key, or else she gets killed by the reverse beartrap. So basically either Amanda or Donnie has to die for the other to survive. And Donnie's fate is out of his hands.
Jeff's traps - Their purpose is clear, to test his ability to forgive, but they still leave Danica, Halden, and Timothy's fates out of their hands, and in the hands of a man obsessed with vengeance against them, so that by the time he decided to act, he was only able to save one of them. The shotgun the key to the Rack was tied to would have killed Jeff if he hadn't found a way around it, and even then it was close.
The mausoleum trap - The way Trevor and Art were pitted against each other, it was set so one would have to kill the other to survive. Art had an advantage there
The spike trap - The trap was for Morgan, but Rex didn't have a chance of survival coz the spikes went through all his major arteries. Not that he didn't deserve it, but still.
The hanging trap - Detective Matthews's fate was out of his hands, unless he killed Rigg to stop him from opening the door. In the end, they did kill each other, Matthews by shooting Rigg, and Rigg by opening the door causing his head to be crushed. Of course this was done to make a point about Rigg not being able to save everyone
The scale trap - Pits Simone and Eddie against each other so one has to die for the other to live
The breathing trap - Again, between William and Hank, one had to die for the other to live. William was fully intended to survive that trap coz all the ones after were for him, and Hank didn't have a chance coz he was a smoker. Hank was basically executed to prove a point to William about his policy. And, it's very clear Jigsaw planned these traps instead of Hoffman coz he appeared on the screen in person for that particular trap.
The hanging trap - Again, William had to choose between Addy and Allen, and could only save one. At least one had to die (both would have if William hadn't chosen)
The steam trap - Debbie would have either killed William for the key to her trap, or ended up being killed by it (the second of which came true), just to prove a point to William about how far people are willing to go to survive.
The Carousel Trap - William was only allowed to save two people, meaning at least four had to die.
William's final test - More than anything it was to give Tara and Brent the chance to exact their revenge on William for killing Harold Abbott, likely Jigsaw's own revenge for denying him coverage for potential cancer treatment, and showing him that the dead do indeed have claim over his soul. He did at least have the chance to beg for mercy, which convinced Tara to back down, but not Brent.
The public execution trap - Again, one of the three had to die for the other two to survive. Either Brad kills Ryan, Ryan kills Brad, or they do nothing and let Dina die - no possible way for all three to make it out alive.
Bobby's traps - Nina and Cale did have some part of what to do in their traps, but Suzanne's trap didn't, her survival was out of her hands and only Bobby could do anything for it. It's clear Jigsaw planned these traps from the flashbacks, but never got around to them before his death. Likely there were others Jigsaw planned but never got around to.
Bobby's final trap - This one deserves special mention because Bobby's pectoral muscles weren't enough to support his weight, thus causing his innocent wife to burn to death with little to no chance of escape, to punish him for lying about being in a saw trap.
- Amanda's traps coz she designed them to be inescapable against Jigsaw's orders
- The hair-pulling trap because it was pretty easy for Rigg to solve them, and there was another meaning behind the trap.
- The pendulum trap, coz Hoffman designed it to be inescapable before he even became Jigsaw's apprentice
- Strahm's glass box trap (with the water), it's been a while since I seen it but Hoffman could have set it up on his own. It was designed for Strahm's execution but Strahm found a way to survive.
- The main traps of Saw V, since they were supposed to work together to solve the traps instead of killing each other, as Jigsaw even hints at the beginning