Sufficiency has to do with whether the statement follows from what we know, and we can reject a premise if it is derived from making a leap to a conclusion when it doesn't have enough strength to support it.

An example is going from seeing one black crow to the premise that all crows are black. One is not enough, it's insufficient to draw the conclusion that all crows are black. Although you can say that at least one crow is black.

Another type of insufficiency is to go through the motions of disproving every one of your opponent's arguments, but actually not verifying that these are truly his arguments. For example, if I'm arguing that a creationist is wrong, and to prove it, I demonstrate that the earth is five billion years old, I may be doing nothing to harm his case if he actually believes that the earth is five billion years old, but has some other point about how it had to evolve with outside assistance. I have been spinning my wheels.