In פרק טז of ויקרא, the Chumash discusses the עבודה performed in the בית המקדש on Yom Kippur. It appears from Rashi's comments (to Pasuk יא and Pasuk יז) that most of the קרבנות brought on Yom Kippur that are part of the special עבודת יום הכיפורים are מכפר only one sin namely, the sin of טומאת במקדש. All other sins of Bnai Yisrael are מכפר on the שעיר המשתלח, which is a goat which is thrown off a cliff and not even placed on the מזבח. Why is there so much complicated עבודה done to get rid of טומאה במקדש, while for all other עבירות the שעיר המשתלח is sufficient.
The answer to this question may be that in truth a perfectly performed שעיר המשתלח could be מכפר all of Bnai Yisrael for all their sins, however, in order to perform the ceremony of the שעיר המשתלח properly, the Beit Hamikdash in which the שעיר המשתלח is prepared, must be in perfect working order. By bringing, טומאה into the Beit Hamikdash, Bnai Yisrael damage the קדושה of the Mikdash. If the קדושה is flawed by טומאה, then the ceremony of the שעיר המשתלח cannot be performed to effect כפרה on behalf of Bnai Yisrael. For this reason, most of the עבודה done on Yom Kippur is performed to be מכפר only the sin ofטומאה במקדש to ensure that the Beit Hamikdash be in perfect spiritual order before the actualשעיר המשתלח is brought and is hopefully מכפר all the other sins of Bnai Yisrael.
This fits in perfectly with the Pesukim in פרק טז. The first 91 Pesukim of the פרק discuss the עבודה of the פר חטאת, the גורל, the שעיר לה', and the קטורת. Aharon says וידוי on the שעיר לה' and the פר חטאת, and he sprinkles the blood of the פר and שעיר on the פרוכת, and before the כפורת. Through this עבודה the Pasuk says he is וכפר על הקודש בני ישראל...ימטומאת (טז:טז). Aharon is מכפר the קודש from being טמא, and is repairing its קדושה which it had lost. Then he sprinkles the blood on the מזבח on which to understand why the כהנים would be separated out in regards to טומאה in the מקדש since they are different than Bnai Yisrael in regards to their access to the מקדש, however, why should the fact that they are כהנים make them need to have a separate קרבן to be מכפר for all sins instead of being מכפר with all of Bnai Yisrael by the שעיר המשתלח. The answer based on what we have already said is that in order for the שעיר המשתלח to work properly, the Kohanim who perform it as well as the Beit Hamikdash must be spiritually perfect. For this reason, it is necessary to bring a separate קרבן to be מכפר the Kohanim first, before bringing the שעיר המשתלח so that when the Kohanim bring the שעיר המשתלח it will effectively allow for forgiveness of Bnai Yisrael's sins.