Leviticus 4:3

if the high priest who is consecrated with oil hath sinned,-as when he hath offered a sin offering for the people not according to the rite, he shall bring for his sin a young bullock unblemished before the Lord for a sin offering.

that brings the people to guilt He promulgated something that was incorrect, and the entire nation sinned unintentionally; or By sinning, the High Priest inculpates every person. This expression is used because it is the High Priest who carries the burden of the Torah. He must be preserved free from sin, because he is personally consecrated to God.

to atone on his sin i.e., to atone for his sin. Since he is a great man, he must sacrifice a bullock, which is the greatest of the offerings.

לאשמת העם, our sages in Horiyot 7 state that these words are restrictive and mean that in this instance the High Priest’s error is treated in the same way as the public’s error, i.e. that he had first ruled (in error) that something was permitted, and had then acted in accordance with his ruling. However, if we were to go by the plain meaning of the text, the message is that if the priests who are charged with teaching the Torah to the people are liable for mistakes they make handing down rulings, then the High Priest who is regarded as the expert for everyone, and whose faulty ruling causes the entire people to commit a sin, is most certainly held to account for his error. As a result, 'והקריב על חטאתו וגו, he will have to bring an offering for his sin.

seeing that sinners are always on different levels morally and ethically, some being more prone to sin than others, the Torah addresses these different groups of people in different ways, each one appropriate to their specific rating in society. The Torah begins with the High Priest, the one who is least likely to commit a sin, and writes: אם הכהן המשיח יחטא לאשמת העם, implying that a sin by the High Priest is most likely the outcome of guilt by the people, their conduct having contributed to his committing such an error. The Talmud (Berachot 34b:29) quotes that if someone makes an error in his private prayer this is a bad omen for him. If, however, the cantor, i.e. the person hired to pray on behalf of the people makes an error, not only he but all those on whose behalf he offered his prayers will suffer the consequences of his error. The sacrifice of a priest who committed an error must be burned and no one derives the slightest benefit from such an offering. Such considerations account for the fact that the Torah did not write here ואשם, “he sinned,” which would have been a warning for the errant person to do teshuvah. Had the Torah phrased its address to the High Priest thus this would not have been appropriate as the error committed by the High Priest did not originate within his heart but his faulty prayer had been due to the sinfulness of the people he represented which had insidiously influenced the words he was uttering.