Ditto on "what kind of cut"? as well as "who cuts it?", and is he upset about literally getting it cut, or that he wants to grow his hair out long, and you want it short?
A good kids barber/stylist will let them feel the buzzers on their hand, have sharp blades so that the hair cut isn't an "epilady" type pulling nightmare, use tepid water (so they aren't burned or frozen), and have some options for distractions (mirror & talking at the minimum...an airplane/firetruck/boat/whatever chair and a basket of toys and music or a video at the upper end).
Has he had a bad experience in the past? Is he afraid of getting cut? Is the noise intolerable (either buzzers or scissors)? Is it a control thing? Does he hate the ticklies? Has he gotten hair dust in his eyes? Once you figure out what the deal actually is, you'll be able to fix it.
i cut my son's hair until he was 3 (can we say sitting on the bathroom counter with shaving cream all over the mirror for him to draw in?). Then one time I misplaced my scissors and had to take him in. They were sooooo much fun, he has never wanted me to cut his hair again. He hated buzzers though, until he was 6, even though he LOVED being able to feel the blade on his hand and watch it NOT cut him, and then watch it CUT his har -he thought the whole thing was quite magical-, but he hated the noise, so the ladies used scissors 99% until last year...when all of a sudden, the noise didn't bug him anymore.
When I asked him why he didn't want me to cut his hair, the answer changed over time. One year it was because the kids place had cool chairs, the next year he didn't want ANYONE to cut his hair (he wanted to grow it out like his friend Miles), and the year after because going somewhere made him feel grownup. All valid reasons. Now I HAVE cut his hair from time to time, and he's been okay with it (ahem, if you don't count the wiggles), but he really prefers someone else to do it. The okay with it, actually means I had to present an argument (like the fact that we were broke...he had a choice between soccer or going to get his hair cut...chose soccer ;)
Good Luck!