@ said:

I applied for it 6/18 for October test, haven't heard anything back, so I think it may not have been approved.

Update: I got the approval letter last week.

This has been the most helpful part for me so far. That just finally clicked for me!

I think I'm understanding this part...

To be a cat is sufficient to be a mammal, but not necessary. Just because something is a mammal doesn't necessarily mean it's a cat, so "cat" is not necessary to be a mammal.

To be a mammal is necessary to be a cat, but not sufficient. If something is a cat, it is necessarily a mammal, so being a mammal is a necessary condition of being a cat. To say something is a mammal is not enough information to infer that is also a cat, so being a mammal is not sufficient to cat.

I applied for it 6/18 for October test, haven't heard anything back, so I think it may not have been approved.

So, if you have to assume that nothing has changed since the last time you checked a fact, it's an assumption, even if you're really sure it's true. If it's implied but not stated, it's an assumption.

Why is it that some arguments are stronger than others?

Some arguments include a fallacy, flawed reasoning, or are incomplete

And what can account for the ordering of these three arguments?

Disney is first because when all the premises are true, there is no other possible conclusion.

Tigers is second because it assumes that an animal that is aggressive and /can/ injure a human is automatically not a suitable pet. Makes sense in the real world, but it's not explicitly stated.

Trash is last because the premises, if true, only suggest the conclusion, but there are many other ways that all the premises could be true but /not/ the claim that the cat did it.

Including examples of non-arguments was helpful.