Why do some cult leaders think they know philosophy well?

They have to act like they do, or else how is anyone going to trust what they say. That’s what they/their PR thought I guess.

Philosophy is the ladder to religion.

Because they very probably do. Philosophy Well, the chairman of the Cult Leader's trade union, is obviously well-known to people like that. Hope this helped.

They believe in answers rather than questions and often feel they've received a special revelation or are unusually wise, or at least wish to portray themselves in such a manner.

They are Delusional Narcissists

Thinking and knowing are two different things.

As you use "cult" in the sense of "an organized group of people you disagree with," it would be helpful to note real-world examples of  such "cult leaders":  Marx, Hitler, Mao, and Pol Pot:  examples of cult leaders who promoted their opinions of truth, which is all most feckless philosophizing does.

If you're reductively equating "cult" only with "religious," then you need to provide examples of that specific type of organized group leaders you find or deem non-truthful, even misstating and misusing one or more philosophies. Your question is in the mode of first order logic, not simply in propositional logic. Thus, unless you're completely unaware of "some cult leaders," it is correct in first order logic to name the "some," as without a given set, the question is fallacious.

Then your question condenses down to theories of mind and motivation, the latter being more of psychologism.  If your interest is genuine re examining and investigating such behavior (which you logically have examples or at least intimations of), then your question is worthwhile.  And if you're simply clueless as to "cults = religions" examples, you might start with reading "Cults:  In too Deep from Jonestown to Scientology."