The command not to wear a garment of mixed linen and wool is found in two places, Leviticus 19:19 and Deuteronomy 22:11.  They are quoted below including surrounding verses related to the subject matter.

Lev 19:19  ‘You shall keep My statutes. You shall not let your livestock breed with another kind. You shall not sow your field with mixed seed. Nor shall a garment of mixed linen and wool come upon you.

Deu 22:9  “You shall not sow your vineyard with different kinds of seed, lest the yield of the seed which you have sown and the fruit of your vineyard be defiled.
Deu 22:10  “You shall not plow with an ox and a donkey together.
Deu 22:11  “You shall not wear a garment of different sorts, such as wool and linen mixed together.
Deu 22:12  “You shall make tassels on the four corners of the clothing with which you cover yourself.

Combining the commands of the two passages we can list them as follows:

• Do not let your livestock breed with another kind.
• Do not sow your field or vineyard with mixed seed.
• Do not plow with an ox and a donkey together.
• Do not wear a garment of mixed linen and wool.
• You shall make tassels on the corners of your clothes.

To the modern mind (and maybe the ancient mind too) these commands appear strange. 

What farmer would try breeding livestock with different kinds?  It’s not a plan for producing strong healthy herds.  For example, you can breed horses and donkeys to produce mules and hinnies, but they are sterile.  What use is a sterile animal? 

Who would sow, for example, barley and wheat together?  They ripen at different times which would make harvesting almost impossible. 

Who would attempt to plough with an ox and donkey together?  They are different heights and strengths and would work against each other making plowing almost impossible.

Mixing linen and wool together, is something that can be done and perhaps such a garment combines the best properties of the two. 

Making tassels is completely unrelated to farming and seems out of place.

This just adds to the perplexity of these commands.  The first three you wouldn’t normally do anyway, the fourth perhaps you would, and the fifth strange.

How are these verses to be understood?  There are two ways to approach these commands.  We can take these instructions literally (which doesn’t make much sense) or we can take them figuratively.  The figurative approach is, I believe, the correct one, and support for this is found with the apostle Paul.  There is a similar command relating to farming found in Deuteronomy 25:4.

Deu 25:4  “You shall not muzzle an ox while it treads out the grain.

Again, we might ask, who would do such a thing anyway?  If you want your ox to keep working and not tire, you would keep it fed.  In 1 Corinthians 9:1-14, the apostle Paul explains that those who preach the gospel should live from the gospel, that is, ministers should be able to make a living from their preaching and not be forced to find secular work.  Part of his argument is based on Deuteronomy 25:4.

1Co 9:9  For it is written in the law of Moses, “YOU SHALL NOT MUZZLE AN OX WHILE IT TREADS OUT THE GRAIN.” Is it oxen God is concerned about?
1Co 9:10  Or does He say it altogether for our sakes? For our sakes, no doubt, this is written, that he who plows should plow in hope, and he who threshes in hope should be partaker of his hope.

Paul is saying that the command, “You shall not muzzle an ox while it treads out the grain,” was not written to be taken literally, but rather figuratively.

Another example in Paul’s writings is found in 2 Corinthians 6:14 where he writes, “Do not be unequally yoked together with unbelievers”. 

2Co 6:14  Do not be unequally yoked together with unbelievers. For what fellowship has righteousness with lawlessness? And what communion has light with darkness?
2Co 6:15  And what accord has Christ with Belial? Or what part has a believer with an unbeliever?
2Co 6:16  And what agreement has the temple of God with idols? For you are the temple of the living God. As God has said: “I WILL DWELL IN THEM AND WALK AMONG THEM. I WILL BE THEIR GOD, AND THEY SHALL BE MY PEOPLE.”

It sounds much like Deuteronomy 22:10, “You shall not plow with an ox and a donkey together”.  When farmers use two animals to plough together, they yoke them together, so it might well have been written, “You shall not unequally yoke an ox and a donkey together”.  With this in mind, Paul’s explanation of Deuteronomy 22:10 is figurative: don’t entangle yourself with those who are Godless.

So, what then is the figurative meaning of not wearing a garment of mixed linen and wool?  We need to understand the framework in which the various instructions in Leviticus and Deuteronomy were given.  God gave these instructions so that Israel would not follow the pagan practices of Egypt and Canaan.

Lev 18:1  Then the LORD spoke to Moses, saying,
Lev 18:2  “Speak to the children of Israel, and say to them: ‘I am the LORD your God.
Lev 18:3  According to the doings of the land of Egypt, where you dwelt, you shall not do; and according to the doings of the land of Canaan, where I am bringing you, you shall not do; nor shall you walk in their ordinances.

Lev 18:24  ‘Do not defile yourselves with any of these things; for by all these the nations are defiled, which I am casting out before you.
Lev 18:25  For the land is defiled; therefore I visit the punishment of its iniquity upon it, and the land vomits out its inhabitants.
Lev 18:26  You shall therefore keep My statutes and My judgments, and shall not commit any of these abominations, either any of your own nation or any stranger who dwells among you
Lev 18:27  (for all these abominations the men of the land have done, who were before you, and thus the land is defiled),
Lev 18:28  lest the land vomit you out also when you defile it, as it vomited out the nations that were before you.

Furthermore, God wanted Israel to be holy as He is holy.

Lev 19:2  “Speak to all the congregation of the children of Israel, and say to them: ‘You shall be holy, for I the LORD your God am holy.

What is God telling the Israelites in these chapters?  He is telling them not to follow the traditions and religious practices of the surrounding pagan nations which were totally opposed to the ways of God.  God is commanding, do not partake of the ways of the pagan world in any shape or form.

The four strange commands relating to agriculture listed earlier:

• Do not let your livestock breed with another kind,
• Do not sow your field or vineyard with mixed seed,
• Do not plow with an ox and a donkey together,
• Do not wear a garment of mixed linen and wool,

are all figurative ways of saying the same thing.  Do not practice pagan traditions and religious practices.  Do not mix such pagan ways with God’s laws.  God is reinforcing His message in Leviticus 18 (quoted above) in agricultural terms that are easily pictured.  As the Israelites went about their daily farming, the commonsense agricultural laws were a constant reminder to them not to partake of the ways of the pagan world.

But what about the last command about making tassels for the corners of their clothes?  The command for tassels is also found in Numbers 15:38-39 where God gives the reason.

Num 15:38  “Speak to the children of Israel: Tell them to make tassels on the corners of their garments throughout their generations, and to put a blue thread in the tassels of the corners.
Num 15:39  And you shall have the tassel, that you may look upon it and remember all the commandments of the LORD and do them, and that you may not follow the harlotry to which your own heart and your own eyes are inclined,

The reason for wearing the tassels is to remember the commandments of God and not follow the ways of the pagans.  This is the same figurative meaning as the previous four commands relating to agriculture.  It’s not out of place at all.  God is just saying the same thing in different ways:  do not partake of the ways of the pagan world.

Conclusion

The commands in Leviticus 19:19 and Deuteronomy 22:9-12,

• Do not let your livestock breed with another kind,
• Do not sow your field or vineyard with mixed seed,
• Do not plow with an ox and a donkey together,
• Do not wear a garment of mixed linen and wool,
• You shall make tassels on the corners of your clothes,

all say the same thing: do not partake of the ways of the pagan world in any shape or form.  That is their figurative meaning.  The literal meaning was not God’s intent:

1 Cor 9:9 Is it oxen God is concerned about?
1 Cor 9:10 Or does He say it altogether for our sakes? For our sakes, no doubt. …