Learning new things makes you a better programmer, always. My first four years, I was a copy/paste programmer. Then I turned 11 and learned algebra. Huge leap forward. Another huge leap forward with trigonometry and calculus. Again when I had access to a library with books that weren't older than me. Another when I finally met other programmers, studied FP and learned half a dozen real languages. Another with statistics, differential equations and linear algebra. And so forth.
The ascent only ever stops if you are employed at a company that has a culture of overwork and no mentoring. But if Gates believed people can't grow, then (true to the headline) he probably made it a self-fulfilling prophesy.
On the other side are the virtuoso's. People who not just through training, but innate ability are at the top of their field.
The rest of us are somewhere in between.
It strikes me as downright ridiculous that there's an infinite ascent to becoming a better programmer, considering that it's trivial to think of examples of people who cannot even master the basics.
I think anecdata in this case doesn't quite cut it.
That said, I very much applaud the sentiment of your message, as I think a lot of people err on the side of thinking that they are innately incapable while diligent practice and learning might get them quite far.
But that doesn't change the, in my opinion, completely sensible observation that some people are just not cut out to be great programmers. Programming is difficult!
From a different perspective - all pro-level athletes got to where they are today with a lot of training. But only a tiny fraction of the global population, if put through the same training regimen, could achieve that pro status.
That's a fixed mindset if there ever was one. He's saying its extremely improbable for someone to go from mediocre to super skilled.
Context: He said this in 1986.
What you are saying is that people can't learn period. Which is not true. 3-4 years is not enough time to master anything, but 10 years might be: