"People don't bother to use critical thinking, to examine statements, to check for sufficient evidence. In short, people want to be ruled."
That's why they accept the wrong idea that rights come from rulers.
"NO! He gives a 'definition;, which is given in a way that is meant to be accepted by everyone."
A definition is meant to be accepted by definition. If you disagree, feel free to have another definition. But that doesn't change the outcome in reality, which can be proven empirically, and that's the argument: With the wrong definition of what a right is, people will manifest suffering in the long term.
"Nature *does* have hierarchies!"
When using the word hierarchy for the concept of order, then yes, nature does have hierarchies. But it's not rulership, because hierarchy doesn't mean rulership anymore, which is your own point.
"I'm sure you know the term "pecking order" - it came about specifically because a hierarchy was observed in chickens."
This is simple violence, which is common among animals because they don't think about it.
"We also have the term 'alpha male' - the male of a pack of animals that rules over the others."
Alpha males don't rule, they lead. There's an important difference between a leader and a ruler. But unfortunately, we no longer use the literal meaning of words, therefore the knowledge is lost over time.
"Depends on what you mean by 'right' here."
A right in the sense of Mark Passio's definition.
"The term 'might makes right' is something we have to deal with."
No, might makes not right, but privilege. Another term people can't tell the difference anymore. A privilege based on violence is not a right. It's an animalistic pecking order. Sapient beings, meaning beings who understand the difference between right and wrong, create privilege exclusively through contracts, acknowledging the free will.
"you're still getting downtrodden by those who don't suffer the consequences of breaking someone else's 'rights'"
You are responsible for the consequences. If violent people don't suffer consequences, it's because people don't defend themselves and surrender.