Why is that, exactly? I grew up in that era, I remember when floppies were actually floppy, and I've been well into computers ever since, but I don't believe I could tell you why. If I had to guess, I'd guess that FAT used a fixed number of bytes for each filename.
The (decimal) 40 characters were A-Z, 0-9, and four punctuation characters -- I don't remember which. Three characters could be stored in a 16 bit word, so a 6.3 filename required 3 words or 6 bytes. The '.' separator was not stored, of course.
The implementers of CP/M or one of those early PC OSes copied the idea but not the encoding and picked 8.3 as a slightly more usable size. Floppy drives were relatively capacious (!) so bigger filenames were reasonable.
The only reason I know this PDP-11 trivia is that end users could recompile the RT-11 kernel to save space, and DEC distributed the OS sources to enable that. The distributed version was written in assembler and had had comments stripped, so it wasn't quite like reading the Lions book, but you could read it if you really wanted to.
I don't think starting early or on your own is a requirement. Like in any field, intrinsic motivation is what counts (IMO).
I started programming in university at... um... 19? As a part of a physics degree. And fell totally in love with it. 20 years later I'm doing it for living and the love really hasn't faded.
Computer graphics is a demanding mistress, you really need to understand why programs and computers work.
Based on my experiences I would consider myself a pretty OK programmer.
I do agree though, I find when I'm teaching my juniors I sometimes have to give a little history lesson as part of it (things like why 8.3 filenames).