The problem is that this robot isn't really very good at his job. He has a tendency to go off on long monologues about the glories of Apple online support options. Go on, give Apple a call and you'll see what I mean.
You can bypass this robot. Here's how. After the robot answers, wait for him to get to his first break and say "Customer Service Representative." The robot will confirm that he'll soon place you in touch with a real human being. He'll then ask you to clarify what topic you're calling about.
This is a trick. Do not respond with a topic. Apple will do practically anything to keep you from proceeding to a more expensive human service representative. They'd rather provide you with speech-synthesized rambles about the glories of particular online FAQs and help pages. They want to help you to "help yourself," i.e. keep costs down.
So, say something strange. Something like "Gallupping Butterflies" or "Indigenous Bicycle Dinosaurs." Make sure that your topic cannot be understand by Mr. Roboto. Once you've stymied him, he'll finally forward you to a real customer service representative.
Of course, the customer service rep may insist on asking you all sorts of questions about whether you are using a Mac or a "PC computer" before routing you on a few more times. Even if you're just calling about a simple Apple Gift Card. (Yes, the example is drawn from real life.) Still, your chances of making a solution happen quickly are often better when you deal with a real person-to-person encounter, and now you know how.