I don't think I said that? But using price incentives allows people to make the choice between spending their money on the same amount of a now more expensive good, or to change their behavior somehow. Hence, a poor person who previously ate beef every day has a number of options such as eating beef only on certain days of the week, eating a smaller portion of beef each day, or eating a less expensive kind of meat.
If we recognize that meat production has negative externalities, then to reduce these externalities we need to reduce meat production, which will necessarily reduce meat consumption. Above you seemed to be implying that the ideal solution would be cessation of meat production entirely - which I have to point out, would also result in poor people being unable to eat meat. So, are you defending the right of the poor to eat meat, or do you want to take the meat off their plates?
Really I assume that what you are getting at is economic fairness, which is not something I bothered mentioning because it didn't seem relevant to the point I was making. But anyway - pigouvian tax schemes are often paired with social benefits. The government uses the taxes raised to either facilitate the social change it wants to create (eg, using a carbon tax to fund transit improvements) or returns the funds to citizens directly as a dividend which offsets the cost of the increased price of goods (in this case, there would be a break even point somewhere around lower middle class where the dividend recieved would be greater than the increased price of meat).