Originally, the offensive definition of the term "basket case" was an amputee who no longer had any limbs. It suggested that the recipient of the insult required carrying around in a basket. So, all right, that's a logical though unkind term.
But now, "basket case" means someone struggling with crippling anxiety or stress. I sort of understand why that would make sense to some, but not entirely, because it is offensive as well as a bit of a stretch logically. Also, in my admittedly limited experience, the turn of phrase has a confusing connotation.
A basket case could be someone who is reduced to tears when faced with a difficult decision.
In "The Breakfast Club", the character called the Basket Case is pretty much just weird.
Either way, it's fairly impolite. So, I propose removing it from our vocabularies or narrowing it down to one straightforward definition.
But, of course, it doesn't really matter what I think about this deemed-improper colloquialism, does it?