To share your analogy: many folks have trouble with algebra. It's not that it's categorically impossible for them to do it; there could be any number of factors (bad math education, home troubles making school more difficult, etc.).
With a lot of time and dedication many of these folks could eventually get pretty good at doing algebra. I've tutored these folks before. Some of them have enough time and dedication to get better at it. But without that (and at least time is outside most of these folks' control), many of them will struggle.
So I don't think the parent comment was saying "Most people can't program in the same way a gorilla can't speak English", but instead "Most people can't program because they don't have the acquired skills to program." I would add that these folks' goal is often not programming but their original job.