Go read the text of the Categorical Imperative.. go do it — you’ll see that the general idea is that in order to decide what is or is not a right action, you need a test of motive. That’s the purpose of the CI, it’s a means of testing your motive for acting to see if it’s a good one or not.
The thing about Kant is that he’s working on a set of background principles that aren’t necessarily clear from the small bit you’re reading for class. Some of his other widely read work is in epistemology (theory of knowledge) and metaphysics (theory of things, in particular people and how we relate to the world) — and he’s come up with some ideas that ground his work in ethics.
One of those ideas is that we’re all beings with the same structures in our minds — and the result of those structures is reason. SO — if you use those structures to reason about morality, you’ll come to the Categorical Imperative .
In fact, it gets even deeper than that — The thing that separates us from all other things is our ability to reason (sounds plausible so far, don’t start with me about animals and reason— I know, I know… ). So, IF and ONLY IF you are a human, you are a reasoning being. Thus, if you look like a human and cease to reason, you cease being a human. I’m not sure what you ARE at that point, but you’re not a human.
If you play the argument out — you’ll see that reasoning about morality (and reaching Kant’s conclusions) is an essential part of being a human being. Thus, because everyone CAN reason, everyone CAN reach the same conclusions Kant did about morality.
I should be clear — neither Kant, nor any other ethical theorist, thinks that all people are successful at obeying the dictates of morality — but, that’s not because they don’t know what they are, they simply choose not to act that way. The also could be misguided about the facts of the matter, the way to go about following the dictates of morality etc.
When understanding the CI, it’s super important to understand that “not everyone agrees with Kant” IS NOT a good objection to the universal formulation of the CI.. it isn’t. I’ll say it now, and I’ll say it over and over again — DO NOT pose this objection… that’s not the point.
The point for Kant is that you, as an individual reasoning being, have the tools to reach a conclusion about what should be done in a particular instance. Because many other things are out of your control, and because the only unqualified good is a good will, you should do the thing for which you have a good motive for action. What other people do, say, believe, etc.. is their problem not yours. That’s why it doesn’t matter that not everyone agrees with the universal formulation of the CI…
In essence, Kant is telling you to keep your own side of the moral street clean — act according to the good will — and you’ll avoid things that are immoral.