So I am a little prejudiced toward mares. Not everyone is. I know people who only want geldings because they believe they are more reliable. They point out that geldings do not have serious mood changes or interpret things differently from day to day because of hormone swings. So they have got a bit of logic to back up their prejudices.
Some people feel that mares are safer than stallions but I do not. You always know what a stallion is thinking about every few seconds so it is easy to predict his behavior and interrupt his thoughts every few seconds so you keep his attention focused on you. Mares are more unpredictable in that they do not necessarily allow you to interrupt whatever it is they are doing. First, they decide whether they are going to pay any attention to you at all. Mares train you to pay careful attention to what they are doing and to what you are doing at all times.
A lot of people say they do not like mares because they have more "attitude" than geldings. They do seem to have more definite attitudes but that does not necessarily mean worse attitudes. The key to working with mares is to understand what is behind their attitudes and to work with them from that understanding rather than fighting with them about who is right.
Mares are naturally protective of their individual territories. If they feel threatened, their first instinct is to get in position to fire both barrels. If a horse kicks in a show class, it is usually a mare objecting because she thinks someone has gotten too close and is coming into her territory uninvited.
When a mare turns her back to you when you open her stall door, she is telling you that this is her territory and you have no rights here. So you just wait at the door until she finally looks back and acknowledges you. Then you step back and acknowledge that this is her home, her space and you respect that. Then she says, "OK, you understand." And she will turn around and allow you to come in to get her.
If you flick a whip at her or try to force her to face you and come over to you, she will expect you to be rude whenever you come into her stall. You will get the cold shoulder every time. Her attitude is, "You’re at my house and you have to behave politely if you want to come in." As I said, mares are very good trainers.
Mares, especially those raised in herds, also have higher awareness of pecking orders. If you start a mare and she is really submissive and nice, she will probably stay that way. If you start a mare that thinks she is at the top of the pecking order, you need to go along with her. You lead the dance without ever letting her become aware that she is not the one doing the directing. You accomplish that by never crossing the line that starts an argument.
When you first turn young horses loose in the arena to play, they often take off and leave like they are making a big escape. Geldings and colts will run and show off with a kind of "look at me" attitude. A mare with a strong personality is more likely to make a really big escape, do a lot of posturing, even kick out. She will look back to make sure you saw her display or her kick. Her attitude is, "Did you see that? Pay attention to what I can do."
Never argue with a mare. In her mind, she is right so if you cross the line that makes her mad, she will fight with you. So you just allow her displays and her kicking every time until she finally decides she wants to come up to you. Then you do a lot of grooming and making friends with her, using rhythmic grooming to establish relaxation and creating the feeling that you are a very nice place to be. If she feels she is at the top of the pecking order, she will think it is totally appropriate that you are grooming her and giving her attention.
As you start heeding her on a lead line, you introduce new pressures in the littlest bites possible so that she continues to feel that everything is her idea. If you stay just below the feeling that she is going to become resistant to the new pressure you are showing her, you will keep the situation under control without ever starting a fight. When you start her under saddle, you continue to show her each new pressure in the smallest possible bites. Never introduce something new that is more than two baby steps away from something she already knows and feels she owns.
A really bad mare may be as bad as it gets. But a really nice mare is as good as you will get. Years ago, we used to take extra horses to show and we would lease them to people for classes. One of the best we ever had was a quarter horse mare named WMD Aloha. We called her Mother. She knew the patterns for every contest. You could rope off her. You could put a little kid on Mother for a pleasure class, tell them to just sit there, and she would listen to the announcer and never miss gait change or change of direction. When the ringmaster stood in the middle with his arms out, Mother knew it was time to line up. Once while I was hauling her, the trailer came off the hitch. Thankfully, the trailer just rolled to a stop without incident. When I opened the door to check on Mother, she had broken a sweat but that was all. Mother was about as good as it gets.
Horses are patternistic but the different sexes seem to feel patterns differently. If a mare is used to a certain pattern of interaction with you, she gets to feeling you owe her that pattern whenever she sees you. Say, for example that you have gotten into the habit of stopping at her stall to give her some scratching and loving every time you walk by. Now if you walk by and do not stop, you will look back to see her frowning and fretting. She is indignant because you neglected your duty.
Geldings, on the other hand, see you coming and say, "Hi, good to see you. Are you planning to stop by today?" If you do not stop, they do not hold it against you. Stallions see you coming and immediately start wondering, "Is there going to be a party?" If you do not start the party routine, they just go back to eating.
Old time horse trainers know there are only two ways you can argue with a mare and neither one works.