Why did Korach challenge the leadership of Moses? Moses took the Jews out of Egypt and through him they received the Torah, so on what basis did he think he could so-to-speak "take Moses down"?

...Korach asked Moses two strange questions.

The Midrash (and Rashi) says that in the course of their dispute, Korach asked Moses two strange questions. One had to do with a tallit, the four-cornered garment which is supposed to have both blue and white fringes. Korach asked a hypothetical question: If the garment is totally blue, need it have blue fringes as well? Then he asked another strange question: If a house is full of holy books, does it need a mezuzah?

Why were these questions the basis of his dispute with Moses?

First of all, let us note that , according to Kabbalah, the color blue represents gevura (strength/restraint). This means that blue represents the descent of spirituality and

G‑dliness from a high place into the lowly physical world. And a mezuzah insures that the house will attract only holy spirituality from above.

So, we have a similarity, then, in the examples with which Korach challenged Moses. With his challenge, he implied that it isn’t necessary to employ intermediaries to bring spirituality into the world. A blue tallit shouldn’t need fringes in order to impart holiness to its wearer, and a house shouldn’t need a mezuzah in order to impart spirituality to its inhabitants.

Korach was saying to Moses that all of the Jews are holy, all of them can directly access spirituality, and why was he, Moses, "lording" over everyone?

There are two kinds of spirituality in the world. One is immanent G‑dliness, which can be felt, understood, and absorbed. In the language of Kabbalah, it is called "permeating light" (ohr penimi). The other kind of spirituality is transcendent. It is beyond us. This is called "surrounding light" (ohr makif). Within Transcendent G‑dliness, there are also two levels of illumination.

Just as a garment rests on our body but not inside it, so the ohr makif can be close to us without penetrating our awareness.

Since we are aware of the existence of this lower level, even though it is beyond our mental and emotional grasp, it is compared by Chasidic literature to a garment. Just as a garment rests on our body but not inside it, so the ohr makif can be close to us without penetrating our awareness. Alternatively, transcendent G‑dliness can be so far beyond us that we have no awareness of its existence, let alone a mental grasp or emotional response to it. In that case, transcendent G‑dliness is compared to a house, with a ceiling beyond our reach.

In either case, in order to turn transcendent spirituality into immanent spirituality – into permeating light, which is useful for us and helps us grow -— we need an intermediary. On the garment, it’s the fringes. On the house, it is the mezuzah. For life in general, it is the rebbe/teacher/leader, the Moses of the generation.

Korach wanted to skip the intermediary. He claimed that we can all directly access transcendent spirituality, and therefore why should we need a Moses or any leader?

But the truth is that even though we’re all equal before G‑d, we have different spiritual levels and tasks. What Korach failed to take into account was that, although all of us have G‑dly souls, not all of us can directly access transcendent spirituality. For that, we need the Moses of the generation, who can take the surrounding light and bring it down to every individual Jew, so that we can all understand the Torah’s message.

[Excerpted from "Inner Lights from Jerusalem" based on the Shem miShmuel and other Chassidic and Kabalistic Sources, translated and presented by Rabbi David Sterne]