Feminism is more than just the project that women are people too… it’s a way of looking at the world using a lens of concerning ourselves with the suffering of others — while valuing differences among us.
Feminists looked at the theories you’ve learned so far (utilitarianism, deontology, virtue ethics, social contract ethics) and realized that, among those theories, there was nothing to account for the way in which women often made decisions within the home. Thus, the ethics of care.
They are explicitly reacting to the seemingly objective standards produced by the other theories. Those theories purport to look at a situation using a particular lens and decide, objectively, what is or is not moral. Instead, the ethics of care advocates that we ought to 1) pay attention to folks around us, looking for a means to help if we can, 2) accept the responsibility we all have for one another’s happiness and well-being, 3) act in a competent manner to help when we can, 4) accept the idea that individuals are sometimes vulnerable, and if YOU are the vulnerable one, you should accept help.
This may result in seemingly ‘unfair’ situations — for example, it may be the case that parents making decisions on behalf of their kids will choose in one circumstance to permit a behavior, and in another circumstance to punish that same behavior. This is because the parent are considering several factors — including the impact on the whole family, the particular combination of child and circumstance, as well as what seems to work best overall at the time.
The advantage to care ethics is that it recognizes the fact that we ARE inter-connected, that we CAN see what others need, and that we CAN help them, and we have a responsibility to do so.
When you think about the actions of feminists in a larger-picture, you see that the ethics of care are at the base of many of their movements toward social justice, fighting the patriarchy, addressing issues of privilege etc. It’s a good thing :).