“Every moving thing that is alive shall be food for you; I give all to you, as I gave the green plant.” Gen. 9:3
God may have made this concession to eat animals for a few reasons I can think of:
1) The reference in Gen. 9:11 of the flood ‘destroying the earth’ seems to indicate damage was done to the planet itself. It would seem obvious that if nothing else, the topsoil would have been severely disrupted, and much of the plant life would have died as well. And so the concession may be to enable Noah and his family to eat rather quickly (simply hunting and cooking an animal, as opposed to foraging, or planting and waiting for a harvest to eat.)
2) The concession may also have been made to satisfy the violent tendency of men, affording them some outlet to those tendencies. Verses 4-6 become telling. Verse 4 informs them to eat the meat without the blood in it (and also possibly not to eat things while they are still alive!) In verse 5 God offers a reminder that they will all in fact die at some point (as God said His spirit would not strive with man forever.) Then in verse 6, God completes His point by reminding them not to murder other human beings – that those who murder will be punished.