Numbers 19:3 - Joseph Benson’s Commentary on the Old and New Testaments

Ye shall give her unto Eleazar Who was the second priest, and in some cases the deputy of the high-priest. To him this service was committed, and not to Aaron, because it was not fit that Aaron should be engaged in any thing that would render him ceremonially unclean, although but till the evening, Numbers 19:8. Yet as it was an affair of great moment, especially as typifying the sufferings and death of Christ, and purification through his blood, it was proper it should be performed by him who was next to Aaron in dignity. The chief priests of our Lord's time had the principal hand in his death. That he may bring her forth without the camp Partly because this heifer was reputed an unclean and accursed thing, being laden with the sins of all the people, and partly to signify that Christ should suffer without the gate, (Hebrews 13:12,) in the place where malefactors suffered.