Every car insurance company comes up with a different strategy to make their business successful. Some of them may choose to insure young drivers only, where they are unlikely to have much in the way no claims bonuses and are deemed a high risk to insure and thus can be charged high premiums. Some of them may choose to insure high performance cars only, where they are able to charge high premiums as well in order to cover the costs of maintaining the car. Some, though, target a segment of the market which are lower risk, tell them that they are paying for people who are higher risk, and hope that whole segment comes to them.
Companies that specialise in lady driver car insurance are, of course, the latter kind of company. Their marketing aims to point out that if you are a woman you are less likely to make large claims compared to men. However, if there have been many claims, your premiums may go up. Which means that you are subsidising those men who have bad accidents and claim large amounts of money. Why not join up with other people who are less risk, and thus claim less, so that you can all enjoy lower premiums?
So, why is it that women are regarded as less risk? Is it because they have fewer accidents? Well, not really, it's actually because the accidents they do have are less serious. There is less damage to the car that they are driving, there is less damage to any other cars involved in the accident, and there is less damage to properties. This means that whilst they may claim as often, women do not claim as much, hence the ability to charge lower premiums. As to why the accidents are less serious, the main reason is that women drive differently to men. They do not try and drive fast, show off to their mates or try driving manoeuvres that are risky.
So, since their car insurance premiums are lower, why would insurer's want to specialise in insuring women? It would appear to be simple maths. If there are lower claims, then the lower premiums do not matter so much, and profit margins are possible. What they do need to do, however, is make sure they have as many customers on their books as possible to make the (admittedly quite small) margins add up to a sizeable profit figure. Thus, they take aim at all women to try and prise them away from anyone else they are taking out car insurance with so that they all join together with other women. It's a simple marketing premise that has worked well enough so that many companies are joining the targeting exercise.