In Likutei Sichos vol. 22 pp. 65-69 the Rebbe explains this maamar from Likutei Torah. In short, he explains the following points:
1- When it says that in the “אָדָם-Man” there is only a negative aspect in his outermost garments, it is referring to the “garment” of speech. There are two types of Lashon Hara-Bad Speech. There is speech intended to cause harm or pain to someone, or is vulgar etc. Then there is speech which is not intended to cause harm and is not inherently bad, but is not spoken for a positive purpose or comes out in not the most appropriate way. The example given is Miriam, who was completely righteous, but spoke about her brother Moshe in a way that was not considered appropriate in that situation. She was punished with Tzaraas. Since the only thing wrong was her outermost “garment” of speech, this is why she received Tzaraas.
2- The fact that in the outermost “garment” of speech there can be something lacking in someone on the level of “אָדָם-Man” comes from a hidden (subconscious) negative aspect, that is not in his reach to correct. This hidden negative aspect expresses itself in his outermost garment of speech. The Tzaraas comes to the person to reveal that hidden negative aspect so that it can be corrected.
3- Because the Kohein is on the level of Chesed-Kindness of Above (in Atzilus), he has the power to reveal an intense Light that is strong enough to even correct the hidden negative aspect. That is why it is necessary for the Kohein to declare “you are pure,” since with his speech he is able to bring down this intense Light that can correct the hidden negative aspect which was the cause of the slightly negative speech.
