Is it correct to say "don't have to care about"? (why/why not) [closed]

I came across the sentence "You don't have to care about your appearance." This sounds wrong to me ("You don't have to think/worry about your appearance" sounds much more natural), but since "You care about your appearance" sounds perfectly normal, I'm wondering if I'm wrong about the first sentence. Can anyone help me suss out what's going on here?

Solution 1:

Worry is fear-based. It is a projection of negative energy.

Care, on the other hand, is a projection of positive energy.

In the word context "You don't have to care about your appearance.", the word "don't" is more likely to be a negative statement. Therefore, worry is more suitable.

However, "You care about your appearance" is much consider to be a positive statement. Thus, we use care instead.