I have difficulty agreeing with most of the OP. Hopefully writing about it would help make things more clear. I’ll start with bringing up the subject of conditioning. It's a vital component to how one reacts. Ivan P. Pavlov is probably the most recognized source I can bring up to have one understand what conditioning is.
"The only person in the entire world who has the power to put you down, is you, nobody else." is a nice thought, but it doesn’t work that way.
"When a person criticises you, certain negative thoughts are automatically triggered.” There we agree. “Your emotional reaction will be created by these thoughts, NOT by what the person actually says to you." I’m not sure you understood what you wrote. Both statements are in contradiction to each other. It goes like this:
“"When a person criticises you, certain negative thoughts are automatically triggered.” When X does Y to you, Z happens
“Your emotional reaction will be created by these thoughts, NOT by what the person actually says to you." When Z happens, it is not caused by X doing Y to you.
“What other people say has no impact on what you feel.” That is incorrect. Conditioning is a learned behavior, and it can quite easily be used to manipulate people to feel negatively about themselves. Conditioning can be applied verbally. This statement can only be valid if conditioning wasn’t real.
“Another person cannot be responsible for making you feel upset or otherwise.” Removing responsibility of a person who is being abusive is abusive in itself.
“No matter how vicious, heartless or cruel comments may be, they have no power to disturb you or create you discomfort.” Yes they can, and they often do. Continue reading, I explain further on that.
“To put it another way, when a person criticises you, the comments they make will either be right or wrong.” That’s a very black-and-white approach to something that isn’t. Half-truths exist and they are frequently used in criticism.
“If the comments are wrong, then you should be questioning yourself as to why you're upset, because there should be nothing to be upset about if the comments are wrong.” What about reputation? Criticizing someone can damage their reputation, change how other people view them. In prehistoric tribal times, if one was criticized, it could mean between remaining in the tribe and being shunned from the tribe. It was life and death.
“Then on the other hand, if the criticism is accurate, there is still no reason for you to be upset or feel overwhelmed, unless you think you should be perfect (Perfectionism is a cognitive distortion).” No, both warrant the reaction of being upset. Again with the black-and-white.
“Sounds simple...” No, it sounds like very black-and-white in reasoning. It’s not as simple as you’ve made it out to be. “yet why do people blame others when criticised?” Full stop. Why blame others when criticized? What approach are you taking now? I can’t go any further than ask those two questions are there are too many directions that this can branch in.
“Now you could fear criticism because you need to feel loved and approved of, but the problem with this scenario is that you're people pleasing,” It’s not the only reason, nor the only scenario.
“another cognitive distortion, leaving little time for you to live your life. Funnily enough, people often find people pleasers less desirable to be around due to a need of constant reassurance.” wherever you got this information was probably pointing this specific situation, of people pleasing. Attributing it to why a person reacts the way they do when criticized is misleading. There are alternative reasons. Stating that would have made more sense.
“What's your take on this subject? Are you vulnerable to criticism, or not? If so, why, if not, why not?” We are all vulnerable to it. There are several different ways in which we react to it. Being upset by someone criticizing you is normal.