"If the anointed priest [the High Priest] will inadvertently sin, bringing guilt to his people..." (Lev. 4:3)
Why should an error of the Kohen Gadol bring guilt to the whole people? It was his sin!
The Maggid explains this idea using an analogy of a person traveling on a poorly-marked road.
If the traveler should lose his way, taking a detour through the fields, his mistake will cost him the time needed to find way back to the road.
But if a wealthy merchant were to make the same mistake, the results will be far worse. When the merchant's many wagons - loaded with heavy merchandise - go off the main road, they will inadvertently mark the mistaken path as if this is the true road. All travelers on the road afterward will make the same mistake and go through the fields.
Now we can understand why the Torah says that the Kohen's mistake "brings guilt to his people." When an individual sins, his sin only affect himself, so he only needs to atone for himself. But when the Kohen Gadol sins, he brings guilt to the entire people, for they learn from him and follow his lead. Therefore his responsibility is much greater, requiring a special korban to atone for his sin.
Adapted from Mishlei Yaakov, pp. 200-201.