First, lots of guys dislike talking on the phone. Or at least, we don't like it as much as girls do. So there's a good chance that phones make him cringe a bit.
Second, if you leave a message, this guy might need a bit more time than you would to figure out what to say, and how to say it. Remember that guys often don't have the same level of verbal skill as girls, and we often get really, really *really* tired of talking, even with people we're madly in love with. So be patient with guys in general about verbal communication -- because I guarantee some guys have been patient with you when it came to stuff that's not your natural skill.
Third, this guy has a life, too, and it doesn't revolve around you every minute of the day. If he's at work, in class, playing basketball, watching a movie, taking a nap or just enjoying some solitude, he has every right to postpone the call until a better time. It doesn't mean he's disrespecting you or ignoring you. It means he has the right to prioritize his life. Depending on the type of call, I don't always expect a reply the same *day* I leave a message.
Fourth, learn to live without your phone. Girls can get addicted to their phones, and place too much importance on it. Turn off your phone occasionally. Leave it in a desk drawer for a few hours. Leave it in the car when you're at work or at school. I suspect one reason this issue bothers you is because you call him, leave a message, then stare at your phone the rest of the day making yourself dizzy: "Why hasn't he called? What's going on? Did I say something wrong? Is he mad at me? Does he disrespect me? Argh!" If this is you, stop giving a little electronic device so much power over your mind. Use your phone *only* when making a call, and check your messages only 2-3 times a day.
Fifth, if you expect him to *always* answer his phone when he doesn't want to, and you're pressing him into promises he'd rather not make, you're being unfair, disrespecting him, and not validating his opinions. You're pushing him away, and you're weakening the relationship. Nagging like that makes me want to break up with a girl. Seriously. I can really like her, but if she's on my case about why-didn't-you-call-me? I want to bail out, and *fast* because I know it'll get worse, and I don't want to hear why-didn't-you-call-me? for the next 40 years.