What is the biblical argument for eating meat, or that vegetarianism is possible but not commanded?

Genesis 9:3 Every moving thing that liveth shall be meat for you; even as the green herb have I given you all things.

After the flood, man had permission to eat meat.

It may be that the climate after the flood would include severe winters and times that plants would not grow readily. The permission to eat meat may have been tied our need to store food for times of shortage.

We see a little of a return to the previous state in the millennial kingdom.

Isaiah 65:25 The wolf and the lamb shall feed together, and the lion shall eat straw like the bullock: and dust shall be the serpent's meat. They shall not hurt nor destroy in all my holy mountain, saith the LORD.

I wrote a paper on this in college: "Do Christians Have a Moral Obligation to abstain from the Killing of Animals for Consumption?". And I think the strongest case to be made is that Jesus chose to feed the multitudes by taking both bread (grains harvested from the earth and prepared for human consumption) and fish (assumed to be wild caught nearby and prepared for human consumption) and used this as a demonstrative tool/miracle, fed those that gathered, on two separate occasions. (Mark 6:37-44,Mark 8:1-9)

Christ could have easily given the fish back and only distributed loaves of bread on both occasions. The result would have been equally miraculous and the crowds would have been filled.

All I would add to what has been answered already is to compare lifespans before and after the Flood (Genesis 5 and Genesis 11). With longer lives, slower growth, and slower aging it follows that lower protein levels in plants would be adequate. After the Flood, declining longevity and rapid aging require higher concentrations of proteins to replace dying cells. God made the more concentrated sources of protein available to us as longevity dropped and aging rapidly increased.

God's Endors*m*nt of Eating Meat

Actually, God specifically ordained that man could eat meat, starting after the flood. The only prohibition in this was to drain the blood:

Every moving thing that lives shall be food for you. And as I gave you the green plants, I give you everything. But you shall not eat flesh with its life, that is, its blood. Genesis 9:3-4 ESV

During the Exodus, God sent quail into the camp to provide the Israelites with meat to eat:

In the evening quail came up and covered the camp, and in the morning dew lay around the camp. Exodus 16:13 ESV

In fact, the Passover was a feast that every Jewish person was under obligation to observe once a year in which they ate the meat of a lamb, so God, once again, ordained and commanded the eating of meat.

Tell all the congregation of Israel that on the tenth day of this month every man shall take a lamb according to their fathers' houses, a lamb for a household. Exodus 12:3 ESV

Vegetarianism

Before the Fall and perhaps up until the flood as well, it is true that mankind was enjoined to eat only vegetables, but that was a temporary command.

And God said, “Behold, I have given you every plant yielding seed that is on the face of all the earth, and every tree with seed in its fruit. You shall have them for food. Genesis 1:29 ESV

It is true that Daniel, Shadrach, Meschach and Abednego did not eat meat during their captivity in Babylon, but that was more likely due to either what kind of meat it was or how it was prepared--perhaps unclean animals that were not kosher for Jews. (See Why did Daniel consider the allotment of food and wine to be wrong for him to eat?.)

But Daniel resolved that he would not defile himself with the king's food, or with the wine that he drank. Therefore he asked the chief of the eunuchs to allow him not to defile himself. Daniel 1:8 ESV

What Jesus Ate

Furthermore, Jesus Himself ate meat, as He observed the Passover meal with His disciples:

And he said to them, “I have earnestly desired to eat this Passover with you before I suffer. Luke 22:15 ESV

On other occasions, He ate fish as well:

They gave him [Jesus] a piece of broiled fish, and he took it and ate before them. Luke 24:42-43 ESV

Paul's Instructions

The most applicable passage, though, is perhaps found in Romans 14. In this passage, Paul address the issue of eating meat that had been sacrificed to false gods. Paul affirms that there is nothing wrong with eating meat, and it is the weaker brother who eats only vegetables in fear that eating meat would be wrong.

As for the one who is weak in faith, welcome him, but not to quarrel over opinions. 2 One person believes he may eat anything, while the weak person eats only vegetables. 3 Let not the one who eats despise the one who abstains, and let not the one who abstains pass judgment on the one who eats, for God has welcomed him. 4 Who are you to pass judgment on the servant of another? It is before his own master that he stands or falls. And he will be upheld, for the Lord is able to make him stand. Romans 14:1-4 ESV

Conclusion

In conclusion, the Bible does not prescribe vegetarianism at all, but records that God actually gave meat to mankind for consumption.