Before getting into the details of command interpretation, I thought I'd give a very simple example of why it's important. Here's an error that occurs all the time. Let's say you have two files, called file1 and file2. You want to create a new version of file1 that has file2 added to the end of it. That's what cat is all about, so you give the command:
cat file1 file2 > file1...wrong
This looks like it should work. If you've ever tried it, you know it doesn't; it erases file1, and then dumps file2 into it. Why? The shell (not cat) handles standard input and output.
As the shell is processing the command, it sees that you're redirecting standard output into file1, so it opens the file for writing, destroying the data that's already in it.
Later, after it's finished interpreting the command line, the shell executes cat, passing file1 and file2 as arguments. But file1 is already empty.
cat reads file1 (which is empty) and writes it on standard output (which goes into file1).
cat reads file2 (which also goes into file1). At this point, cat is finished, so it exits.
file1 and file2 are identical, which isn't what you wanted. But it's what you got.
Some versions of cat give you a warning message in
cat: input file1 is output). This might lead you to believe that
somehow cat was smart and managed to protect you. Sadly, that's
not true. By the time cat figures out that an input file and an
output file are the same, it's too late: file1 is already gone.
This bit of catty cleverness does have a function, though: it prevents
cat file1 file2 >> file2
from creating infinitely long files.