It's exposure to the air and the consequent oxidation that's the problem.
Think of it this way; linseed oil is a 'drying' oil, meaning that it oxidises and polymerizes (turns into a varnish) very readily.
This is considered to be a desirable thing, because linseed oil is used as a wood finish.
Linseed oil remains a liquid while it is being shipped and stored in bottles, but when it is spread thinly on wood and exposed to air, it gums up and then hardens.
Oil stored in bottles isn't a good indicator of its resistance to gumming/varnishing, because the bottle contains only a limited amount of oxygen.
ATF contains antioxidant additives to further prevent oxidation even when exposed to air, which is one of the reasons I'm so enthusiastic about it.