1. Fear. Horses are naturally claustrophobic, so the idea of something wrapped tightly about their barrel isn't exactly at the top of their list. Young horses freshly started under-saddle (or improperly started under-saddle) are particularly prone to this. They freeze and tense up suddenly, and sometimes hump their back in preparation to explode. In my experience, time is the best cure. I'll roundpen a young horse and play all sorts of games with them while they carry a saddle and grow accustomed to the new weight and feel of a saddle and cinch. I'll play around with the cinch, tightening and loosening it and gradually increasing the amount of time the cinch is tight. Desensitizing the horse to the feel of a cinch is the best way to help a fearful horse overcome the fear of having something tightened around her barrel. If your horse is fearful of being cinched, working on gaining her trust on the ground is absolutely essential. Do not get on this horse's back or you run the risk of being bucked off - if she's not comfortable with a saddle, she is not going to be comfortable with a predator on her back.
2. They're annoyed. This is usually the result of a cinch being done up rudely - all at once. This is akin to tightening your belt up to the tightest hole possible, immediately...you wouldn't like it either! First off, while a cinch should be snug, it should never be tight. If your saddle fits correctly and your balance as a rider is good, your cinch should not need to be tightened until the horse stops breathing - the correct fit will keep the saddle in place, as will your balance. On the other hand though, neither should the cinch be flapping wildly in the wind, or you risk the saddle moving too much (particularly with an unbalanced rider or at higher speeds or more complicated movements), creating rubs and sores. When you do do up the cinch though, be respectful towards your horse about it! Do it up in stages, and do it up snug, but never tight. I'll tighten a cinch until it's snug, circle the horse, re-tighten, circle some more, re-check the cinch, then mount-up. If your horse does turn around to nip you at cinch-tightening time, you can do a number of things. First off, keep the horse out of your space, either through tying her up shorter or (preferably) through body language. For the latter, you can earn a horse's respect through playing the same ground games she plays out in the paddock with her herdmates. When your horse comes in to nip, you can play these same games - ie. use body language - to create a "bubble" of personal space your horse stays out of. I use "chicken wings" (lol). If I feel a horse coming in, I'll raise my elbows as if they were chicken wings, flapping. The horse either stays out of my space or runs into my elbow as she comes into my space. This makes it her responsibility to stay out of my space, without faulting me; I'm not coming in and hitting her, she is coming in and running into me - it makes a difference to the horse! Another thing you can do is, every time your horse comes in and swings her head around to nip at you, is to surprise her with something positive, such as a carrot. This way, she comes in with ears laid back and leaves with ears pricked forward and a good attitude. What happens last starts to happen first, and pretty soon you've got ears pricked forward rather than back, with a bad attitude becoming a good one. She learns that being cinched up isn't such a terrible thing after all.
3. Your horse is associating being cinched up with something she dislikes that happens under-saddle. With my Quarab, Silver, he became cinchy when he started associating being cinched up with the pain of working in an ill-fitting saddle that was causing chiropractic issues. Once the chiropractic issue was eliminated and the saddle was fit better, he stopped being cinchy because he enjoyed his work under-saddle! Take a step back and evaluate what you do under-saddle: is the horse over-worked or not warmed up or warmed down sufficiently, resulting in tired, sore muscles after a ride? Does the saddle fit? Are there chiropractic, or other physical issues, going on? How are your hands? Your seat? What your horse has to say about being caught, about being tacked up, about being mounted, among other things - all reflects upon your work under-saddle with him.