Genesis 9:3

Every moving thing that liveth shall be meat for you
That is, every beast, fowl, and fish, without exception; for though there was a difference at this time of clean and unclean creatures with respect to sacrifice, yet not with respect to food; every creature of God was good then, as it is now, and it was left to man's reason and judgment what to make use of, as would be most conducive to his health, and agreeable to his taste: and though there was a distinction afterwards made under the Levitical dispensation among the Jews, who were forbid the use of some creatures; yet they themselves say ^F11, that all unclean beasts will be clean in the world to come, in the times of the Messiah, as they were to the sons of Noah, and refer to this text in proof of it; the only exception in the text is, that they must be living creatures which are taken, and used for food; not such as die of themselves, or are torn to pieces by wild beasts, but such as are taken alive, and killed in a proper manner:

even as the green herb have I given you all things;
as every green herb was given for meat to Adam originally, without any exception, ( Genesis 1:29 Genesis 1:30 ) so every living creature, without exception, was given to Noah and his sons for food. Some think, and it is a general opinion, that this was a new grant, that man had no right before to eat flesh, nor did he; and it is certain it is not before expressed, but it may be included in the general grant of power and dominion over the creatures made to Adam; and since what is before observed is only a renewal of former grants, this may be considered in the same light; or otherwise the dominion over the creatures first granted to Adam will be reduced to a small matter, if he had no right nor power to kill and eat them; besides, in so large a space of time as 1600 years and upwards, the world must have been overstocked with creatures, if they were not used for such a purpose; nor will Abel's offering the firstling and fattest of his flock appear so praiseworthy, when it made no difference with him, if he ate not of them, whether they were fat or lean; and who will deny that there were peace offerings before the flood, which the offerer always ate of? to which may be added the luxury of men before the flood, who thereby were given to impure and carnal lusts; and our Lord expressly says of the men of that age, that they were "eating and drinking", living in a voluptuous manner, which can hardly be accounted for, if they lived only on herbs, see ( Luke 17:22 ) though it must be owned, that it was a common notion of poets and philosophers ^F12, that men in the golden age, as they call it, did not eat flesh, but lived on herbs and fruit.