You absolutely have the right to hurt other people for self defense and self preservation.

Sure, but I'm not talking about self defense. I'm talking about people choosing to eat animals when they could eat something else. I'm not telling people they can't protect themselves from an animal attacking them. I'm saying they shouldn't eat animals (or humans). If it is literally a matter of life or death, like in your subsequent example where somebody is going to starve to death, I think it often enters a case by case basis.

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Would you tell a starving person not to kill and eat a goat?

Would you tell a starving person not to kill an eat a human? Veganism doesn't answer the question of "is it OK to murder an innocent to save yourself". It just says you shouldn't be treating livestock different than humans when it comes to answering that question.

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that is what true denial of life to others looks like.

This is very backwards. Telling people not to kill is not the "true denial of life". Killing is the true denial of life.