What's so special about אשי יהוה, and לחם אלהיו that the Kohanim are to be Holy because of it, and the ba'al mumim can't bring these?
Rav Hirsch explains the concept of מום at length in Vayikra - Emor 21:17
The entire explanation is too long to put here, but I will try to give a brief summary. I have been asked to edit in the English for the Hebrew used by Rav Hirsch.
First, he points out that there are three different classes of מום which have different effects and reasons
- an actual מום which would prevent an animal from being brought on the מזבח. This would cause any קרבן (Korban - sacrifice) that such a kohen brings to be pasul. One concept is that the kohen represents the person who is bringing the קרבן and as such, he must be seen as
being of the same level of godliness as that to which he is to raise the human being who is represented in the offering ...
A person is to regard himself as being brought as a korbon and as such, the kohen must also regard himself as a korbon and subject to the same rules.
It is evident then that he appearance of the כהן המקריב (the kohen who brings the sacrifice) must not be in any way a contradiction of the character that makes the קרבבן (sacrifice) worthy of הקרבה (being brought on the altar).
- שאינו שוה בזרעו של אהרון (That he is not like the normal descendants of Aharon) He must be seen as a normal member of the family and not afflicted with deformities (that would still not make the קרבן considered פסול (unfit). Here he does not make the קרבן invalid, but he still is עובר (violates) a מצוה (commandment), whether a לאו (negative) or an עשה (positive) (it is a dispute which).
It is not the afflicted and the infirm, not the blind and the lame, the disfigured and crippled, the broken and the sick, for whom the Jewish Altar is erected, so that weary, burdened humanity can drag itself up to it to find compassionate consolation or even miraculous healing. It is life in its completeness, in its freshness and its strength, which there is to gain consecration to an active life of God-serving deeds, and therebye acquire the everlasting freshness of youth and unbroken forces of life.
THe kohen must be shown (at the time he approaches the mizbeach) as being a representative of the family after Hashem has poured His blessings upon the Bnai Yisrael and be seen as such a representative by those bring the animals.
- םשום מראית עין (because of mar'is ayin - appearance), these should not do any עבודה (service), but if they do so, it is כשרה (kosher) and they have not transgressed in any way (Bchoros 43a & b).
THe kohanim must be the representatives of and the exemplars of the promise of Hashem to brife life and health to those who serve Him.
כי אני השם רופאך (I am Hashem your Healer) And it is this promise and the conditions attendant to it which priests and offerings have continuously to illustrate and give a a clear idea of in the Sanctuary of this Torah.
That is why it must be perfect complete men - not בעלי מום (those who have a defect) - who have to perform the offerings.
The kohen is to represent that which everyone strives for and, since people form their ideas of the spiritual from what reaches their eyes, the kohanim must always strive to appear to be like the goal that is being approached.
Rav Hirsch summarizes this concept and finishes
It is in its harmonious, healthy and attractive aspect, not deformed or unpleasant, that Man is to picture life in the proximity of Hashem.