Manual and Automated Testing are both Extensions of Human Thinking
If you're comparing, you're missing the point
A computer can check for an expected result, and do so much more often and quickly than a person, but only in the way it's programmed to. Testing spans many more activities than making assertions. All which comes before the pass/fail check, like examining biases and questioning design decisions, is part of a manual, human, process.
The question of whether manual or automated testing is "better", in a general sense, misses the point. Is it better to cut with scissors or a chainsaw? Tools have different areas of application, and the one you use depends on your context.
So the false dichotomy that I’m referring to here is this notion of a split between human testing and automated testing such that we can ask which is better in some categorical sense. [1]
Jeff Nyman reframes the question, asking whether it's better for humans or tools to do the testing, and in doing so highlights the answer: we need both.
Tools act as extensions our thinking
We employ tools to extend our capabilities, in fact, Our Thinking May Not Happen Only In The Brain
References:
[1] A False Dichotomy of Modern Testing - Jeff Nyman, 2018