From the Sources
אמר רב יהודה אמר רב אדם הראשון לא הותר לו בשר לאכילה דכתיב (בראשית א, כט) לכם יהיה לאכלה ולכל חית הארץ ולא חית הארץ לכם
Rav Yehuda says that Rav says: Meat was not permitted to Adam, the first man, for consumption, as it is written: “And God said: Behold, I have given you every herb that brings forth seed, which is upon the face of all the earth, and every tree, in which is the fruit of a tree that gives forth seed; for you it shall be for food, and for every animal of the earth, and for every fowl of the air, and for everything that creeps upon the earth, in which there is a living soul, every green herb for food. And it was so” (Genesis 1:29–30). It is derived God told Adam: Eating vegetation is permitted to people and animals, but eating the animals of the earth is not permitted to you. (Sanhedrin 59B)
In last’s week’s Parsha we learned that Adam was given permission to eat from all fruits, vegetables and grasses on the earth, except for the Eitz HaDa’at Tov v’Ra, the tree of the knowledge of good and evil. But people were NOT given permission to eat meat. Only after the flood was permission granted to mankind to eat meat.
כָּל־רֶ֙מֶשׂ֙ אֲשֶׁ֣ר הוּא־חַ֔י לָכֶ֥ם יִהְיֶ֖ה לְאָכְלָ֑ה כְּיֶ֣רֶק עֵ֔שֶׂב נָתַ֥תִּי לָכֶ֖ם אֶת־כֹּֽל׃
Every creature that lives shall be yours to eat; as with the green grasses, I give you all these. (Bereishit 9:3)
There are several reasons given for why Noach was allowed to eat meat. Firstly, before the flood, man and animals were “equal” in that both of them had been created by Hashem. However, after the parsha, the status of animals was lowered as they had been continued in creation, (or “recreated”) by Noach. For this reason, people were given permission to use animals for food. It is stated that before the Mabul, people were much healthier. The air was purer. We can see that from the fact that they lived much longer before the flood than after the flood. Before the flood they did not need meat to be strong. After the flood they did. This is another reason given for why permission was granted to eat meat after the flood.
It is also stated that the moral standard that Hashem expected of people after the flood was lowered, as Hashem had seen the depravity of people. This was another reason given to eat meat. In fact, it was the evil king Nimrod who was the first to actually eat meat, and he persuaded other people to also do the same. These ideas are discussed in an ‘Ask the Rabbi’ on Aish HaTorah’s website, here.
How to eat it
Two ways, really. Either, make a point of being vegetarian last week, for Bereishit, and then eating meat. On the other hand, acknowledge that it was Nimrod who was the first to actually eat meat, acknowledge that he was a “bad guy”, and remain vegetarian for another week.