Statements like "I cannot jump 30 feet vertically" are different than "We cannot approve your loan at this time" or "We cannot admit you to our university" as the second two examples really mean "We don't want to."
Is there a term for this?
Statements like "I cannot jump 30 feet vertically" are different than "We cannot approve your loan at this time" or "We cannot admit you to our university" as the second two examples really mean "We don't want to."
Is there a term for this?
Based on the vernacular used on ell.SE The difference between Can't and Won't is one of implication. Can't implies something different than won't does.
That link also covers the definitions of the two words in deference to each other, which is sort of a tacit question here.
The implication of the two words is the subject of an article on inc.com which talks about can't being substituted for won't as a sign of weakness so perhaps substitute / substitution is another way to describe the relationship between these two words.
It is also a recurring joke on the TV show Archer wherein the main character is a bit of a jerk about the whole thing.
"Won't" is a contraction of "will not". So the difference between "cannot" and "won't" resolves to the difference between "can" and "will".
Can is about certain indisputable qualities or facts. In your question, physical forces such as gravity on earth or ceilings prohibit the ability of unaltered, unassisted people to jump 30 feet in the air.
Will implies desires, wants, hopes and intentions. This implies a person to have these intentions.
In the case of a loan approval or a university admission, there are certain rules and regulations in place which must be followed. The use of the word "can't" implies that these rules are the prohibiting factor, not a human decision. They may not be as indisputable as physical forces, but they are incontrovertible for loan company or university admissions staff. Therefore "cannot" is used correctly here and does not mean "won't".
On the other hand "I can’t have dinner with you tonight (despite having no other plans)" probably means "I don’t want to have dinner with you tonight" and "won’t" could be used here. But it’s a lot less confrontational to use "can’t".
Cannot in the given context means choose not to (for unspecified reasons).
So to answer the question, Is there a term for using "cannot" when one really means "doesn't want to?"
Yes, it's called: "choosing not to." Sometimes referred to as: "deciding not to."
It's a matter of framing the conversation, not proper usage.
"we cannot provide you a loan at this time" - assuming they are providing loans to others, so are not out of cash - means "we don't want to". But it tends not to invite a debate.
As an American having lived in the UK for a few years, it feels much more standard in the UK, which seems a more formal society. "we cannot" does not invite the question "why not". In America, you are more likely to hear phrases like "we would love to, but because of your credit score are unable to" which does invite more debate - i.e., "how can you look at a single number when I have been a good customer for 20 years?!!"