Why don’t lowercase letters come right after uppercase letters in ASCII?

With that context, I always found it strange that the designers of ASCII included 6 characters after uppercase Z before starting the lowercase letters. Then it hit me: we have 26 letters in the English alphabet, plus 6 additional characters before lowercase starts: 26 + 6 = 32. If you know anything about computers, powers of 2 tend to stick out. Let's take a look at the binary representations of some characters compared to their lowercase counterparts.

Tyler Hillery

I only have a middling understanding of the rest of the article and thus the ultimate reason why ASCII includes those six characters between Z and a, but I think it comes down to making certain operations on uppercase and lowercase letters specifically more elegant. In some deep crevices of my brain all of this makes sense, but I find it very difficult to truly understand and explain as someone who knows little about programming.