I honestly dont see any point in listing reasons why humans arent algorithms. I only need to conclude that giving rights to immortal, easily copied intelligent algorithms would create problems for human society to decide we shouldnt give them rights.
Then you reject the idea that's stated front-and-center as the starting point of their reasoning without giving it any thought. At least they listed a good reason why it might be correct.
You're turning the burden of proof on itself. The authors claim that humans are only algorithms, it's their job to prove it before mounting an argument based on it.
The authors assume the idea for launching an argument, but OP assumes the opposite idea. There's no point to contrasting each other because they are both unproved. At least the web page gaves some reasons why you should entertain the idea.
You reasoning completely breaks down if we accept that we've already given rights to algorithms (=humans) since the invention of rights.