Feminism is a theory that has taken on many meanings over the years. A simple Google search of "types of feminism" will take you on a journey through many, many different forms of feminism. From the more familiar "radical feminism", to the much more contradictory "Bourgeoise feminist". In the words of Cameron Vasquez, "There are as many feminisms as there are feminists". However, this quote is simply not true. Feminism is quite simply the theory that people of both sexes should have equality. And while such a practice seems simple in theory, it is a much harder and much more important one to grasp. Feminism is not about advancing one woman to a position of higher standing. It is about elevating all people of all genders to a place where they are equal. However, that cannot be achieved without seriously dismantling an entire system of discrimination.
The term "intersectional feminism" was coined by Kimberle Crenshaw, in her essay "Mapping the Margins: Intersectionality, Identity Politics, and Violence Against Women of Color". The essay was a commentary on how traditional feminist movements were often in the favor of straight white middle class women.
To say that women want to have the same rights as men becomes a much more complicated statement when you factor in which women and which men are holding the power. A woman who is lower class and Latina will never reach the status of a white male billionaire, simply because of many power structures that are in play, whether her gender factors into why she is discriminated against or not. By this same token, a white middle class woman could be equal to an african american man by means of status, and gender according to a traditional feminist theory, but there is once again still a power structure that does not allow for equality within a fixed system. Intersectionality is essentially striving toward people of all races, classes, genders, sexualities, and a variety of other binaries having equality.
For feminism to work as a theory, it must include equality for people of all walks of life. One cannot effectively dismantle a corrupt power structure whilst still allowing parts of said power structure to remain. Intersectionality and equality are synonymous terms within the feminist movement. To consider oneself a feminist without considering oneself an intersectional feminist, is to practice a form of feminism which is not sustainable, or even truly practical.