Here's a scenario that plays out every day in arenas and round pens across the country: Something frightens, upsets in some way or causes pain to a horse and the horse reacts negatively.
Let's face it, horses are just not wired like humans, they don't think like we do or process situations in a complex fashion the same way a person would. Though horses can become explosive, so to speak, and dangerous, such a thing really isn't an inherent quality in equines.
So, how do we label a horse as a "problem"? There are generally two types of problem horses, those with issues related to ground manners and those who we encounter trouble with when they're under saddle. Each must be dealt with differently and how you approach each horse's issues depends largely on the horse itself.
I approach ground work issues by maintaining a calm, cool demeanor and allowing the horse to have every opportunity to do the right thing (which should be true for any training issue). If he chooses not to, there must be consequences.
For instance, biting. One of the most dangerous behaviors in horses in my opinion, no one enjoys being bitten. Any horse who chooses to attempt to bite me (note the word "attempt") will be met with a sharp tap on the muzzle simultaneously with a firm verbal reprimand in the form of a loud "NO!". If consistent, this behavior will wane quickly, but consistency is the key. Never, ever allow your horse to bite. It's not funny, it's not cute and one day that horse will hurt you.
With horses that pull, rush or otherwise get pushy, giving such a horse room will allow him the opportunity to decide to stay out of my space. Should he choose otherwise, I will be ready to send hm backwards several steps to establish my "herd" position. He does not have a right to invade my space, ever. Previously I've covered leading, tying and trailer loading, so we'll move on to issues under saddle.
When saddled, the three most common bad behaviors, in order of severity, are rearing, bolting and bucking.
My aversion to the horse that rears is rather well founded: I'm not fond of being flipped over on. Period. But for most horses, it's either pain related or a learned behavior to get out of work, making the fixes relatively simple. The first step I'll take, of course, with a horse that habitually rears is to have a thorough vet check performed, paying special attention to the cervical spine and the back (including withers loin and hip), mouth and feet/legs.
If there is no physical reason for the horse to act out, we get back to work on prevention. There are a few simple rules for dealing with an obstinate rearer: Going forward and requesting lateral movement, disengaging the hindquarters, is the quickest means to bring a horse out of a rear. Don't grab hold of his face, lean forward and encourage the horse to move. Getting off is NOT an option. If you have ever dealt with a horse who has successfully unseated a rider in this manner, you'll agree.
Fear is a whole different matter, though I don't necessarily consider a fearful horse a problem horse. Generally, once the horse comes to understand that he's going to be sent forward and rearing isn't getting him out of work, the behavior will cease.
Next on my list is the serial bolter. While not quite as high on the danger scale in an enclosed space (round pen, arena, fenced field, etc) as a horse who rears, things can go wrong in a hurry when you're out on the trail and your horse decides he's leaving. Taking off isn't such a big deal to correct if the behavior occurs anywhere he's ridden ~ in other words, if you can abate the problem in an arena or round pen. It's the horse that only bolts with you intermittently on the trail that is the real troublemaker.
When dealing with a runaway, the absolute worst thing you can do is panic. Unless something horribly dangerous is imminent, stay with the horse and ride it out. If the sequence tends to start with a spook, go back to ground training and work on both fear and stand-your-ground issues (otherwise commonly known as "spook in place" training). Your first step should be to reassure the horse and make him face that fear. Be it a wind blown tarp, a barking dog, scary dark trash can or even that odd looking rock near the arena gate, he has to understand it isn't going to harm him and he need not try to get away from it. He can be afraid but must stand his ground. Once he's mastered that, get back on and put those same principles to use from the saddle.
Something I cannot stress enough is how important your "Whoa!" command must be in your training at ALL times. If the horse tenses up and begins to exhibit behavior which leads you to believe he's getting ready to run, remain neutral and ask him to halt. That word means freeze and don't move until you are told. NO questions asked.
If he's the to take off without warning, working through the problem can be more of a challenge because it's next to impossible for you to feel it coming. Be sure he's not grabbing the bit between his teeth (if he does, bump him to dislodge it while distracting him with your weight, seat and legs), rock back and begin a circle in a safe location out on the trail ~ in the arena, it's easy. Send him forward fairly hard, but control the direction and speed. Be consistent, just as with any training issue. Eventually he'll overcome whatever fear he has or there will be zero fun in trying to get away with the naughty behavior.
Last we'll address bucking, though 99% of the time it's not as huge of an issue as the previous two topics. Most horses cannot buck without being able to get their heads down, and a majority of horses really don't give more than a half-hearted crow hop (which definitely can unseat an unsuspecting or unbalanced rider) when under saddle.
Just because a horse does buck when turned loose to play or does so on the longeline doesn't necessarily mean he's going to try tossing his rider. I'm not fond of allowing a horse to buck when it's time to work, so a reprimand is in order at that time ~ every time.
Now, what to do with the horse who habitually tries to unseat you? For starters, don't let him get that poll below his withers. If you do, he's got the leverage to really let loose and you've already lost much of your ability to prevent the buck. For the "playful" buckers, I'll stick a sidecheck on them and soon it's too much of an effort to fight against it. Gradually you work such a horse for longer periods of time without the sidecheck and soon you can remove it altogether.
But, if bucking is a more serious endeavor for the horse and is accompanied by attempting to twist or rear, I'll throw the horse (figuratively speaking, of course) into the tightest circle he can maintain while staying in a trot or canter, always continuing to maintain forward impulsion and not allowing the horse's head to drop below my hands. That part is important.
Forward = lacking the ability to rear...head not allowed to get lower = lacking the ability to buck, unless he's a contortionist. Most are not, so as long as you follow those rules you should be just fine.
Remember, any issue you do not feel confident enough to resolve on your own should be handed over to a skilled and competent professional trainer. There is nothing wrong with enlisting help, especially when in the end it's likely to mean the difference between you getting hurt or your horse overcoming his issues.