Don't the majority of people think there is
nothing morally wrong with eating meat?
This is correct. However, as discussed in the title page, truth is not democratic. The Earth does not become flat just because the majority of the population thinks that it is.
One hundred years ago, racial segregation was considered acceptable by the majority of the United States. Two hundred years ago, slavery was considered morally acceptable by the vast majority of the world. Two thousand years ago, it was considered acceptable to feed innocent people to lions for public entertainment. If you look further back, it was considered acceptable in some parts of the world to have servants buried alive with their recently deceased master.
In each case, morality progressed because a small number of people looked at the ethics of their society, and concluded that it needed to be improved. Now is no better a time to think that we have it all figured out than were any of these other points in history.
Follow up questions:
Do you want to make eating meat illegal?
What about how other animals kill and eat each other?
Doesn't the Bible say that humans have dominion over the animals?