שעירי יום הכיפורים

The focal point of the service in the Bais Hamikdash on Yom Kippur is the Avoda of the two goats; the שעיר לה‘ and שעיר לעזזאל  . The Gemara tells us that these two goats must be identical in physical features, price and must be purchased in the same transaction.  A lottery was cast, and one goat was brought as a Korban to Hashem with its blood sprinkled in the Kodesh Hakadoshim and the other was sent off to a desert wasteland and thrown off a cliff.
Why the need for identical features?
Why do we need the lottery to determine each goat’s fate?
A regular Korban Chatas that is sacrificed to atone for a sin has a certain process for it to be a complete Korban.
First, סמיכה; the sinner places his hands upon the animal confesses his sins and symbolically transfers the sins to the animal.  Afterwards there is the slaughtering and sprinkling of its blood, this is when the actual atonement takes place.  Finally, there is the Haktara the burning of certain parts of the animal upon the Mizbaiach.
On Yom Kippur, the Kohen Gadol confesses the sins of all of the Jewish people upon the שעיר לעזזאל . This includes all types of sins, even ones that a typical Korban Chatas cannot atone for, like intentional sins or ones that deserve capital punishment.
Usually one animal is enough to handle all aspects of the Korban.  However, on Yom Kippur due to the sheer magnitude of the sins this Korban bears, there is a need for two animals. Therefore, the jobs are split, the Sforno explains that because the שעיר לעזזאל has been loaded down with so many grievous sins it is not fitting that it be used in the Bais Hamikdash, it is sent off to the wasteland.  The atonement that is gained through the slaughtering, sprinkled blood and burning of the Korban must be via a different goat; the שעיר לה’
The two  שעירים of Yom Kippur are really one Korban, therefore they must be completely identical.  There cannot be any distinction between the two animals; since they are same there is no way other than an arbitrary lottery to determine which goat performs which task.  On Yom Kippur the goal is for of Bnei Yisroel to achieve atonement for all their sins.  Since the Kapara is on a much larger scale than usual, two goats are needed to fulfill the job of one Korban.