You don't seem to recognize what critical thinking is or does. If you did, you wouldn't have written those words.
Critical thinking involves using a form of thought that reliably produces sound conclusions, conclusions that those proficient in the process can agree upon by following fallacy-free argumentation. It is absolutely possible to tell if this method was used or not, but probably only if one can do it proficiently himself. An apt analogy is the addition of a column of numbers. If you know the rules of addition, and execute them properly, you can go from addends to sum every time, and others doing the same thing using those same rules will come to that sound "conclusion as well." Furthermore, they can look at one another's work and confirm its soundness.
Now suppose somebody comes along unskilled in addition. He says that the sum of that column of numbers is infinity (this stands for "therefore God"). He is told that there is no way to get from a finite number of finite numbers to "infinity" using addition done properly (this stands for critical thinking), and he is told, "I did use correct adding as best I could. You're assuming that because you didn't get infinity as a sum that all people will conclude that. I don't know if you added properly or not. There's no way for me to tell."
Too arrogant? Usually I get that when I say that something is true that a faith-based thinker doesn't recognize can be known with confidence. That's arrogance to those who think that all opinions are equal, because to them, opinions are always arbitrary. None are better than any other, since they're all just opinions.
And, of course you failed when you went to the personal. This is what it's source calls the pyramid of disagreement. The three bottom levels are instant fails.
Compare that to my response to your post. I explicitly refuted your central point, namely that you did use critical thinking. I described what that was and what it can do, and that if it didn't do it for you, then you weren't doing it properly. I added the analogy of adding to illustrate that when there is a proscribed manner of thinking as with critical thought and addition, it is possible to apply the method if one knows how, to determine whether he has arrived at the correct sum, and to know that one is correct even if others who cannot follow do not.
And there you go again, imputing some character defect in your collocutor. You dove to the bottom half of the pyramid again.
I suspect that this is not the proper venue for you, or if it is, that you either stick to the DIRs that exclude people who might disagree with you, or try to understand the people that seem to vex you in your misunderstanding of them. You submit your opinions to the marketplace of ideas on a public discussion forum, and then bristle at the reactions you get, as if people are being mean to you. No, they just have a different method of deciding what is true about the world than you do, and different values regarding what is appropriate conversation. It's a different culture.