I preferred 1e druids over 2e, when they were a distinct subclass like paladin, rather than shoved into a cleric with a nature focus. Oddly, though, some of the characteristics that were carried over intact remained opaque and arbitrary. One of these is the equipment restrictions. 1e simply states that they have “an inability to wear protective armor of metal” (1e PH, p. 21). Their weapons, without any explanation, are limited to “club, dagger, dart, hammer, scimitar, sling, spear, staff”. For 2e, they tried a little harder to justify these same restrictions by stating explicitly a druid can only use “natural” armors, with weapons still unexplained (2e PH, p. 35).
I don’t see how iron is any different in “naturalness” than leather. The distinction they seem to want to make is “organic” or “biological”, so let’s treat that as the reason. Either way, it still shines no light on why this would apply to armor, when weapons like scimitars still violate the rule. This is another example of trying to retrofit a somewhat rational design scheme onto a hodge-podge of peremptory rules: It is incomplete, inconsistent, and unsatisfactory.