As humans in a human-supremacist society we're all privileged and socialized by those aspects of society that attribute value to humans and humanness and devalue nonhuman animals. We're all privileged by the systemic, institutional, and individual practices that exploit nonhuman animals. This is speciesism, and we're all speciesists.
There's no point denying reality. Our very humanness is defined in opposition to nonhuman animals. As long as the structure of our society privileges humanness and exploits nonhumans we're going to be speciesists. By the very fact that we're human, we benefit from human privilege. There is no such thing as a "non-speciesist" under a human-supremacist system.
To dismantle the system of human supremacy we need to be anti-speciesists. This is were veganism comes in. Even though as humans we're still privileged by human supremacy, as vegans we can challenge some aspects of the human-supremacist system and can therefore be anti-speciesists. For instance, by not using animal-derived products, goods, and services we challenge our own human privilege and that of others around us. We can work to challenge our own individual beliefs, attitudes and actions that support or perpetuate speciesism. Yet, being privileged and socialized by a human-supremacist system means challenging our individual unconscious and passive speciesism is not an easy task.
There is a network of institutional structures, policies, and practices that create privileges that benefit us humans and exploit animals form target nonhuman populations. Many of these privileges are taken for granted and are invisible to us. For instance, we rarely think of the millions of nonhuman animals who are killed everyday in the US by our transportation system or the destruction this system causes them collectively through the fragmentation of their communities.
Obviously the oppressive effect that our transportation system has on nonhuman animals is not always conscious. Systemic speciesism, like individual speciesism, can be unconscious or conscious policies, procedure, or practices that displace, control, capture, exploit, or exterminate nonhuman animals. Systemic speciesism is supported by institutional power and by powerful (often unexamined) ideas that make speciesism look normal and justified. Systemic speciesism allows individuals to practice speciesism unchecked.
(My thoughts on speciesism above have been adapted from the definitions and descriptions of the ideology of racism found in: Animal Rights/Human Rights, by David Nibert; Dancing on Live Embers, by Tina Lopes and Barb Thomas; "Definitions and Descriptions of Racism," by Sharon Martinas (Challenging White Supremacy Workshops); and Teaching for Diversity and Social Justice, by Maurianne Adams, Lee Anne Bell, and Pat Griffin.)