Before the Flood, God gave no permission for man to eat the flesh of animals. The original diet laid down in genesis 1:29 and 3:18 consisted of nuts, fruits grains and vegetables. This order of things prevailed until after the Flood. Then, because vegetation had been destroyed by the Flood, God allowed the use of flesh food for the first time. It was for this purpose that the clean animals had been taken into the ark by [sevens pairs] and the unclean by twos (Genesis 7:1, 2).
Even though Genesis 9:3 seems to be an unrestricted permit to eat any kind of animal, please note that it was not without limits. God said, "Even as the green herb have I given you all things." In the same way that God had given vegetation, so now He gave flesh. But all vegetation was not good to eat. There were weeds and poisonous plants that could not be eaten. In the same way, God proceeded soon afterward (Leviticus chapter 11) to show that certain animals were not good for food and should definitely not be eaten.
It is also interesting to note that this instruction was given to Noah immediately after leaving the ark. Since it takes two (both male and female) to propagate a species and only two of each unclean animal were saved in the ark, it is certain that God did not give license to eat the unclean animals. If He had, the unclean species would have been exterminated, and none would exist today -- Seventh-day Adventist Bible Commentary.