Nombres 8:17

For every first born is Mine. The first born were Mine by the rules of justice, since I protected them among the Egyptian firstborn. So I took them for Myself — until they strayed with the [golden] calf. Now I have taken the Levites.

For every first-born of the sons of Israel is Mine, whether of man or of beast: in the day that I slew all the first-born in the land of Mizraim, I sanctified them before Me;

כי לי כל בכור, I had already owned the firstborn whose duty it had been to perform the tasks now given to the Levites. The reason that the firstborn had originally been charged with the duties was that they were the most distinguished members of their respective families and one delegates those to represent one before one’s lord and master, before G’d.

ביום הכותי כל בכור בארץ מצרים הקדשתי, the reason why I required them now to undergo the procedure of being redeemed from their sanctity and the duties that were part of this that from the day I had sanctified them, was that they were not supposed to engage in mundane activities, such as earning a livelihood, at all.
Firstborn male animals that are acceptable as sacrifices on the altar may not be used for mundane purposes, i.e their owners must neither let them perform work, not shear their wool and use it for themselves. This was in order for Me to have demonstrated their holy character. These regulations were imposed in order to justify these firstborn not being killed along the firstborn of the rest of the Egyptians and their herds. Having been part of the Egyptian culture, and having been the most distinguished in their respective families, they should, ordinarily, have become part of Psalms 78,49 calls the משלחת מלאכי רעים, “the wrath inflicted by the band of deadly messengers.” The surviving firstborn humans and their offspring, in order not to lead a life of idleness, therefore have to be “redeemed,” so that they can at least lead normal lives. G’d therefore accomplished this by the stratagem known as פדיון, redemption.