According to the Merriam-Webster online dictionary, the meanings of responsible, answerable, and payable are
responsible: liable to be called on to answer
answerable: liable to be called to account
payable: that may, can, or must be paid.
They all include the meaning of obligation rather than the straightforward meaning of the suffix, the one of capability as in durable, whose meaning in the online dictionary is
durable: able to exist for a long time without significant deterioration in quality or value.
In the case of responsible, it seems possible to argue that the suffix gives to the word the meaning of freedom or opportunity that the adjective able has as in
You are able to skate on the lake today. The ice is thick enough.
Then, the sentence below may mean he has the right to decide everything about recruiting and training.
He is responsible for recruiting and training new staff.
But, such interpretation seems impossible for the other two words.
Why does the suffix able sometimes have the meaning of obligation in words such as payable or answerable?
(I found two similar questions. One is about how to tell whether the suffix has the meaning of ability or that of obligation. My question is about why the suffix has the meaning of obligation. The other has not been given a proper answer because, in my opinion, the words used as examples are uncommon words.)