There was no reason Sasori could want to kill her back then, nothing indicates she really standed in his way. Yet in the battle to the death he had to kill her anyway, which he didn't do though, while it was clearly stated he could do this with ease. And the reason for that was also mentioned.
It's not that Sasori is an evil person. but when it came to killing chiyo he couldn't do it mentally although physically he could easily have done it. Sasori is just misunderstood and Since he grew up with mere puppets representing his parents and with granny Chiyo it just wasn't the same. That's why Sasori became the person he was. He never grew up with parental love, or much love at all. But once he found the art of puppet making he found his craft, something he could do while trying to hide from the pain he felt inside and instead he let that pain merge with his art of puppets which is why he eventually made puppets of his parents so he could somewhat have a family although it was never a thing.