Explain to someone that programming isn't just all "if"s and "else"s
Obviously your friend is using a bit of hyperbole, and in truth, however annoyed you may be by his blithe dismissal of our entire field, he may not be open to being persuaded.  You may have to resign yourself to not "winning" this argument.  From what you've written, this is what I suspect is the real answer.

For what it's worth, he's not, strictly speaking, wrong.  Data storage and branching are a huge portion of what computers actually do.

But if you still want to attempt to capture him, you might point him towards image recognition.  Sure, it's "if this then do this" in theory, but two different images of birds will share not a single pixel in common, so how do you teach a machine that can only look at one pixel at a time to identify one?


  "Computer Science is no more about computers than astronomy is about telescopes." -misattributed to Edsger Dijkstra


Of course, even if he concedes the complexity of the problem, that's still a ways away from seeing the joy in trying to solve it. I'm not sure there's truly a way from here to there if he's not interested in taking an honest look.