There is that tendency. There are also owners who encourage it, and delight in bragging about their 'evil mare'. Mares will kick or nip to drive away another mare's foal, or kick to drive a stallion away when not in season, and if allowed, react to people moving around them, especially touching around their flanks, in that way. My experience is that when a new person gets a mare, the mare will 'try out' that behavior ('try out' is how it looks to the casual observer, but it is totally instinctive, and teaching animals to not do it, is basically like teaching someone not to blink when a baseball is coming straight at their eyeballs, NOT doing it will break down quickly if not constantly reinforced).
I think most of the time when mares really do act bad, and aren't just badly trained, they have cystic ovaries, or other painful reproductive problems. Most of the time, it's training. MOST.....
I've seen a few very, very severe cases of cystic ovaries. One was really horrible - the animal would very resignedly stagger along through every ride, and occasionally just couldn't take it any more and would blow up. The owner 'could not afford' a vet appointment. So she longed the horse for an hour or two before every ride. Most people assumed the problems were being exaggerated(you could look in the ring and see this horse shuffling slowly along with its head down most of the time, and completely miss the occasional explosion), or that they were due to the lack of skill of the rider. It was horrible to watch that poor animal stagger along. When the vet was finally called, he said the ovaries were so bad, he wanted to send pics of them to a veterinary journal. He also said the animal would have been in constant, severe pain.
They say 'a mare never forgets' - being ridden in pain for a long time, the animal develops defensive habits that remain long after the pain is removed.
There is a typical form to the muscles of the hind quarters and how the tail is held, a typical way the animal moves off after mounting, and usually, a very typical behavior under saddle - the animal goes from a pretty continuous sullen unresponsiveness or very, very slow response to rider signals, to occasional explosion of bucking or similar reaction. Sudden bucking in a very quiet animal might be due to cystic ovaries or related, painful problems.