What do you have against my binary and ternary definitions of existence and moral obligations though? Don't you see how a) they usefully match your actual experience b) they seem to eliminate any "mysticism" in Rand's words?
To answer your question: because beliefs is what we have. We don't really know things. We believe things. And we use language to communicate our beliefs. If you define knowledge to be "true justified belief" then you'd be stuck as you wouldn't ever be sure of something 100% so you wouldn't "know" anything by that definition.
And before you ask how come we know mathematical truths are true, it's because they are part of the language we have chosen to use, eg logic and math. If we used some sociological mumbojumbo arguments to convince each other eg of institutional oppressio then maybe mathematical theorems underpinning statistical results wouldn't be as certain in that context.
Again, I haven't read Kant beyond the "categorical imperative". I just noticed that people usually face all these difficulties because they fail to precisely DEFINE all their terms. This set of definitions just seems to best match what's really going on.