Aaron’s Sons Didn’t Wear the Robe
At the dedication of the Mishkan, the portable Sanctuary in the desert, two of Aaron’s sons brought an unauthorized offering for which misdeed they were punished: “Fire came out from before G‑d and consumed them, and they died.”
What, precisely, was their sin?
The Midrash cites several infractions for which they were punished. One of them was their failure to wear priestly garments. The Midrash then askes, which one of the priestly garments were they not wearing? And the answer is the Me’il-Robe.
The Midrash is obviously recording an oral tradition that it was the robe that they refused to wear, but that begs the question, why, of all the priestly garments, did they refuse to wear the robe?
Second, commentators pose another question: The Kohain Gadol-High Priest would wear eight garments. An ordinary priest would wear four. Yet, Aaron’s sons wore seven of the eight, which compounds our original question. If they decided that they, too, wanted to be like High Priests, why did they leave out the Robe?
Bells and Pomegranates
We can suggest an answer based on two features of the robe’s design: It had bells on it which were intended to make noise as the High Priest entered the Sanctuary. The Robe also had pomegranate decorations hanging from its hem. This feature too had a function, as the Rebbe explains.  It was to remind the High Priest that his role was to “bring into the Sanctuary” and elevate even the lowliest Jews, about whom the Talmud states, “Even the sinners of Israel are filled with Mitzvos like a pomegranate is filled with seeds.”
The Rebbe explains that one of duties of the Kohain Gadol was never to lose sight of the people he is serving. Even as he enters the holiest place in the world and is enraptured with G‑d’s presence, he had to bring along those Jews who were, figuratively speaking, on the bottom of his robe. It was necessary for him to make a lot of noise and fanfare to attract those lost souls. And although G‑d is expressed through a hallowed silence, when saving the lives of those lost souls we must resort to extraordinary measures.  
The Rebbe further states that this message is especially relevant in our day and age, for we are a “bottom of the robe” generation. We are at the bottom of the robe, otherwise referred to as the “heels of Moshiach.” At this juncture in time, it behooves us to be especially outgoing and vocal in reaching out to these “bottom of the robe/pomegranate” Jews
Souls on Fire
As the sons of Aaron entered the Holy of Holies they felt so enraptured that they believed themselves qualified to don the garments worn only by the High Priest. However, they recognized that it would be improper for them to wear the Robe itself. When entering into the Sanctuary, and experiencing the most intimate relationship with G‑d, they felt it would be impertinent to bring these “bottom of the robe/pomegranate” Jews, who were so wanting in spirituality, into their experience. It was also disrespectful, in their view, to make noise in a place that bespeaks holy tranquility.
Their goal was to enter into a powerful spiritual relationship with G‑d.  They yearned so for this experience that they were prepared to have their souls leave their bodies.  That is exactly what transpired. The fire from G‑d that consumed them was a manifestation of the passion and fire of their souls. As Chassidus explains, their death was not really a punishment but rather the ultimate realization of their spiritual ambitions.
In the grip of their obsessive Divine passion they felt that they should wear the vestments of the High Priest to enhance their spiritual experience. Perhaps they eschewed the Robe because it so directly symbolized the second role of the High priest: to reach out and embrace those Jews who were so distant from their natural spirituality. This second role they refused to embrace.
Difference Between Breastplate and Robe
One could ask why they felt comfortable with the idea of wearing the Choshen-Breastplate, which had the names of all the tribes etched into its jewels. Did this not represent bringing all of the Jews into the Sanctuary?
The difference is that the Breastplate, which represented all of the Jews, was worn on their hearts. On one level, it represented how they could feel the pain and the needs of all the Jews.  However, wearing the Robe required taking this empathy to the next level; to not be content with feeling the pain and needs of others, but to reach out to them and lend a helping hand.
Robe of Tzedakah
All of the above is hinted in the words of the prophet Isaiah (61:10) in which he describes the future Messianic era:
“I will rejoice intensely with G‑d, my soul will exult with my G‑d, for He has dressed me in the raiment of salvation, in a robe of tzedakah-righteousness has He cloaked me...” 
The prophet refers here to Tzedakah as a robe. The Alter Rebbe explains in Likkutei Torah that the Robe symbolized making a tangible difference in the world for the Robe would be followed by the pealing of its little bells, generating a physical noise; a metaphor for a palpable impact on this physical world of ours. Tzedakah, more than any other mitzvah, has that tangible impact. It is for this reason that our Sages state that the final Redemption will occur and be hastened through acts of Tzedakah.
No Sleeves
It is interesting that the Rambam informs us that the priestly Robe lacked sleeves. What is the spiritual significance of this fact?
If wearing the Robe symbolized the High Priest leaving his comfort zone to lend a hand to others, we can understand the reason the Robe had no sleeves.
Sleeves cover the arms, symbolizing the notion of giving to others in a concealed fashion. Anonymous giving is considered a virtue in the Talmud. However, we are also told that giving publicly has the potential to be even more virtuous because it makes a powerful statement of righteousness, setting an example for others to follow. The Talmud states that one who inspires others to give is superior to the one who only gives from himself.
The essential difference between these two forms of giving is that when one gives privately it enhances the individual spiritual level of giving and is good for the benefactor’s soul because it removes some of the ego that can be a driving force for people to give publicly.
On the other hand, public giving propagates more Tzedakah and more people are helped.  That has a more powerful impact on the world and prepares it for the final Redemption.
How do we solve this conundrum? Give anonymously or publicly?
The Rebbe resolved this question by proposing a solution that is the best of both worlds:
Give large amounts publicly and then add on more privately.
By removing the sleeves of the Robe that symbolize hidden giving and affecting the world, the impact is maximized and helps prepare us for, and indeed hastens, the Final Redemption.