The reason why horses kick at you is simple – it is because they feel threatened. Kicking is a self defense mechanism that usually creates space allowing horses to get away from danger. It is unusual for horse to just start kicking for no readily apparent reason – but get after one with a flag, a rope or a whip and they will likely kick out.
If a horse is surprised, afraid, or uncomfortable they may kick, when they feel trapped they will sometimes kick. However, when a horse is feeling confident and at ease it is very unlikely they will resort to kicking.
Some of the typical situations where horses kick at people include, the horse being surprised, the person trying to force the horse to pick up its feet, move it out of the way (usually suddenly or aggressively) when approaching a foal with it’s mother, either the foal, which is unfamiliar with the world and lacking confidence or the mother, protecting its foal, may kick out.
A certain clinician was advising people that “it’s okay to whip your horse with a carrot stick because horses will kick each other and with greater force than you can hit one“. Such advice has nothing to do with horsemanship but may be used by some harsh trainers, or people who don’t understand equine behaviour
When horses are in a herd they quickly develop a hierarchy, the herd boss will eat and drink first and the others will make way. If they don’t, they may get a stern glance, a twitch of an ear, the threat of a bite, an actual bite, the threat of a kick or a kick – there is almost always a progression from a warning to action.
If your horse kicked at you, or actually made contact it probably told you what it was going to, you probably weren’t paying attention. On the other hand if you are using a flag, whip, rope, etc., in a training session, the horse may be feigning a kick as a form of protest, and that will soon dissipate. Horses accommodate to human behaviour, at times to their own detriment, becoming numb or “desensitized” to situations that are threatening at first blush.
Tom Dorrance famously remarked something to the effect of “we shouldn’t be concerned with what happened, but with what happened before what happened, happened“. We often trigger responses from horses that we don’t intend, and if we are aware of how that happens we start looking for the triggering happening.