‘My people are destroyed for lack of knowledge.
‘Because you have rejected knowledge,
I will also reject you, that you shall be no priest to me.
Seeing you have forgotten the law of your God,
I also will forget your children.'
It is possible to see this as addressed to Israel, seen as priests to the nations (compare Isaiah 61:6), or alternately it may be seen as addressed directly to the priesthood. But even in the latter case we must remember that from YHWH's viewpoint Israel had no distinctive priesthood, for their priests were not descended from Aaron. They were charlatans originally appointed by Jeroboam I (1 Kings 13:33). Thus as far as He was concerned the distinction between priest and people was blurred. The priests were merely ‘of the people'.
His accusation is that His people are ‘destroyed for lack of knowledge', i.e. because they do not know YHWH as He really is (Hosea 4:1) and are ignorant of the covenant. It may be that this was being laid directly at the priests' doors, for it was their responsibility to teach the Law, but the failure was undoubtedly partly due to the fact that the priests had been appointed by the people (through their king) rather than by God, so that the people had to share the blame. Whoever is being addressed (whether priest or people-priests) the charge is that they have culpably rejected knowledge, and especially knowledge as found in His Law, and therefore will themselves be rejected so that they can no longer serve YHWH in a priestly function, or indeed in any other way. It is always dangerous to ignore genuine truth. And because they have forgotten the Law of God, He will no longer watch over and care for ‘their children' (either their own children or the people seen as their children). He will in return ‘forget' them.