This verse is interpreted by Paul in 1Cor. 9.8-10 and yet few Christians understand it (or, possibly, I understand it wrong). I am fairly sure I grasp what Paul meant. Here is Paul’s take on this command only given once in Dt. 25.4:
Do I say this merely on human authority? Doesn’t the Law say the same thing?
For it is written in the Law of Moses: “Do not muzzle an ox while it is treading out the grain.” Is it about oxen that God is concerned? Surely he says this for us, doesn’t he? Yes, this was written for us, because whoever plows and threshes should be able to do so in the hope of sharing in the harvest. (1Cor. 9.8-10)
The key word in Paul’s proof that Dt. 25.4 speaks to the situation that he and the other apostles were in, I propose, is “thresh.” “Thresh” here is used metaphorically to refer to inflicting pain. Threshing is the removal of the grain from the inedible stem. It involves using an animal alone or with a weighted cart physically (and violently) to separate the wheat from the stalk. The Hebrew word for “tread” in Dt. 25.4 is only found here and means to thresh or tread.
Paul says he and the other apostles were involved in plowing and threshing (metaphorically) when they spread the gospel and so should expect to be supported financially. Focusing on “threshing,” this would have been Paul’s corrective words in his letters and rebukes in person toward other Christians to correct ungodly or errant behavior.
Returning to the context of Dt. 25.4, we see hypothetical punishment in the form of 40 lashes (usually 39) by an officer of the judge (probably Jewish High Priest). So, in Deuteronomy, we have a sanctioned judgment and punishment by the priests who didn’t really get paid for this type of service, that is, civil judgment (notice vs. 1).
Priests lived off the sacrifices (meat) of the Israelites’ offerings and tithes. Civil matters are separate from the temple sacrifices but ultimately maintains the nation’s justice and therefore appropriate for priests to preside in this type of procedure. I propose Dt. 25.4 as a sort of ‘court costs’ for sustaining the officials who serve in this judicial process as well as those who dole out the punishment. The executor of the lashes would have had to be respectful to the recipient (vs. 3) and yet impersonally punish the offender. All these arrangements suggest governmental ministers and funding for this judicial service since Moses is giving instructions not to a few people but to a nation.
What Deuteronomy seems to be saying is the one threshing (giving the blows of punishment) should share in the benefit by receiving compensation for his position. Paul recognizes the text is speaking metaphorically and not about oxen.