Man's diet before the flood was simple:
Then God said, “Behold, I have given you every plant yielding seed that is on the surface of all the earth, and every tree which has fruit yielding seed; it shall be food for you; and to every beast of the earth and to every bird of the sky and to every thing that moves on the earth which has life, I have given every green plant for food”; and it was so. (Genesis 1:29-30, bold emphasis added)People and animals were vegetarians right after creation— in fact, death itself was nonexistent until the Fall— but when Adam and Eve sinned, their eyes were opened and they became ashamed of their nakedness. In order to hide their nakedness, God Himself slaughtered the first animal in history and used it to cover them.
After that first animal was slaughtered, men also began to slaughter animals. However, Scripture does not indicate that people in the Post-Eden world began slaughtering animals for food. Rather, people began slaughtering animals in the Post-Eden world for the same reason that Abel did: in order to offer up an offering to God (Genesis 4:4).
Perhaps people also slaughtered animals for other non-sacrificial reasons, but the bottom line is this: Scripture does not indicate anywhere that man's diet changed after the Fall. In fact, the evidence is very strong that man's diet did not change at all until after the Flood, when for the first time, God permitted man to kill to eat. God said to Noah:
Every moving thing that is alive shall be food for you; I give all to you, as I gave the green plant. (Genesis 9:3)Why did God permit this change? One possibility is that as people continued devolving over successive generations (and as people began to live shorter and shorter lives), the nutrition that came from meat must have become necessary. It might be helpful to compare this dramatic change in diet to the dramatic change that happened in Moses' time, when God forbid the marrying of close relatives. Why? Because man was continuing to devolve— and marrying close relatives did not produce enough genetic variation (for more information see Who Was Cain's Wife).
God tacked on only one exception for anyone who chooses to eat meat. God said to Noah:
Only you shall not eat flesh with its life, that is, its blood. (Genesis 9:4)The reasoning for this seems quite clear (and simple): eating bloody meat is not the most healthy of decisions. Blood also serves an interesting role in forgiveness: without the shedding of it, there is no forgiveness. Since blood plays this crucial role in redemption, the idea of consuming it is all the more disgusting.
The Post-Flood Era ushered in many changes, including a change in man's diet. Indeed, man's diet (or, at least, the diet of believers) would undergo two more major changes in the Post-Flood World: God would limit the type of meat man could eat (Leviticus 11:1-12), and then once again allow all meat to be eaten (Acts 10:9-16).
The Origin Of The Death Penalty - Genesis 9:5-7
How The Relationship Between Man And Animal Changed After The Flood
Did Noah Gather "Vegetarian" Food? - Genesis 6:21
The Cave Men of Genesis - Genesis 4
The Cycle Of The Seasons - Genesis 8:22