When discussing some of the laws relating to Kohanim, the Torah says "לא יטמא בעל בעמיו להחלו," which means, according to some commentaries, that a Kohein may not defile himself in order to bury someone, because this represents a חילול, a desecration, of his position (ויקרא כ"א:ד'). The Targum Onkelos on this Posuk learns that this is not referring to any ordinary Kohein, but to the leader of his people, presumably meaning the Kohein Gadol. The question is why the Posuk would single out the Kohein Gadol specifically, when we know that the Kohein Gadol and a Kohein Hedyot (an ordinary Kohein) are equal with regards to the law of not becoming defiled (טמא) or touching things that are טמא. Furthermore, we already know from the first Posuk in our Parsha (שם פסוק א') that it is forbidden for any Kohein to become טמא. Why should our Posuk say anything about the Kohein Gadol?
The Sefer שי לתורה quotes an answer from Rav Yitzchak Zev Soloveitchik. He explains that if a Kohein Gadol and a Kohein Hedyot are walking together and they come across a מת מצוה, meaning a dead person who has nobody else to bury him, and therefore one of these two Kohanim must bury him and become טמא, the Rambam (פרק ג' מהל' אבל הלכה ט') says that it's preferable that the Kohein Hedyot takes care of the מת מצוה and becomes טמא, because the Kohein Gadol has a higher Kedushah. In other words, even though the technical laws of becoming טמא are equal for a Kohein Gadol and a Kohein Hedyot, there is greater desecration of Kedushah if the Kohein Gadol becomes טמא.
For this reason, Rav Soloveitchik adds, the Torah says the word "להחלו," which means that there is a desecration of Kedushah, or what we call a Chillul. The Posuk therefore means that a Kohein Gadol cannot become טמא, and the reason is להחלו, because the desecration of his position is worse than the desecration of the Kohein Hedyot's position since he has greater Kedushah. Whenever there is a higher level of Kedushah, there is greater potential for Chillul.