Why do we say
It's detrimental to your health.
but
It's bad for your health
How does the preposition work here?
Why do we say
It's detrimental to your health.
but
It's bad for your health
How does the preposition work here?
Detrimental as an adjective comes from a noun, the -al suffix can help you spot this. So to say something is detrimental means it causes a detriment, and we would normally say something causes a detriment to something else.
Bad is an adjective, and we generally understand it to describe an ongoing state not an event. The preposition is telling us what is in that state, so it's bad for your health.
I hope that helps.
As a native speaker, I don't see any obvious logic here. If someone can formulate a rule or set of rules that explain all such choices, I have not seen it.
As Lambie says "to be bad to {someone}" means to mistreat or be hostile to that person, while "to be bad for {someone}" means to affect that person negatively, as a food or a situation.
It's detrimental to {something}.
is a very commo9n and natural expression, while
It's detrimental for {something}.
while not wrong nor significantly different in meaning is far less common. These patterns spread and become locked in by imitation, I think. "Detrimental" does suggest a decrease in something, and so is perhaps most naturally paired with "to" where it can indicate that decrease, so that might be a bit of logic. But if so, it is not one that native speakers think about routinely.