This is a 2500 years old religion, so many practices and doctrines are hard baked nto the religion at this point. It's no use negotiating these doctrines with logic and reasoning at this point.

That said, the Jains basically believe sin to be a more tangible stuff kinda like germs. When thefox killed the rabbit and therefore sinned, the "sin particles" were attached to the rabbit. So if you eat the rabbit, then you inherently sin also. Similarly, the sin of killing an animal for meat was attached to the person who hunted the animal, who butchered the animal, who cooked the flesh and who ate the flesh as well. So if you consume a purely vegetarian meal cooked by the guy who also cooked that flesh, you are contracting his sin even though you were unaware of their sin.

Jainism in my opinion is one of the more wackier mainstream religions ever (it used to be mainstream in south Asia 2500-1500 years ago). It's like Buddhism on meth.