Purpose of the Service of Vayikra 16/2

The Service of Acharei Mot

Exegetical Approaches

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Atonement for the People

The main focus of the service was to achieve Atonement for all of Israel. Any part of the service that has to do with purification of the Mikdash is just a means to the ends of Atonement

Sources:Rav Sadia Gaon, Rambam (Shgagot 

Purification of the Temple

The main focus of the service is to purify the Mikdash from impurity. All issues that deal with atonement are just a byproduct of rectifying the impurity in the Mikdash.

Sources:RashiVayikra 16:1Vayikra 16:2Vayikra 16:3Vayikra 16:11Vayikra 16:16Vayikra 16:23Vayikra 16:32Vayikra 16:34About R. Shelomo Yitzchaki, ShadalVayikra 16:1Vayikra 16:8Vayikra 16:16Vayikra 16:30About R. Shemuel David Luzzatto

Purification and Atonement For a Greater Purpose 

Both purifications of the Mikdash and Atonement for the people are essential to the Avodah and are equally driving the service of Yom Kippur.

Sources:R. Yosef Bekhor ShorVayikra 16:1Vayikra 16:2Vayikra 16:3Vayikra 16:4Vayikra 16:5Vayikra 16:8Vayikra 16:10Vayikra 16:17Vayikra 16:32Vayikra 16:33About R. Yosef Bekhor Shor, Nitziv,  Ralbag