In 1947, at the 11th IVU World Vegetarian Congress, Donald Watson, representing the Vegan Society, gave a speech on veganism where he said "that the vegan believed that if they were to be true emancipators of animals they must renounce absolutely their traditional and conceited attitude that they had the right to use them to serve their needs. They must supply those needs by other means."
This is an argument for liberation, as opposed to an argument for rights or equality. As a liberation-oriented approach, veganism addresses the structure of the oppression of nonhuman animals.
In renouncing the "traditional and conceited attitude" that we can exploit other animals, vegans renounce what we'd today call speciesism. In Animal Rights/Human Rights, David Nibert writes that speciesism is an ideology: "a set of socially shared beliefs that legitimates an existing or desired social order." Nibert explains that speciesism is created by the construction and prorogation of ideas that devalue other animals. Thus, speciesism isn't a failure to apply "equal consideration" to other animals, as purported by equality theorists (e.g., Dunayer, Francione, Singer).
In practice, veganism means renouncing the benefits that come from the exploitation that speciesism is constructed to naturalize. Theory and practice are one; you can't "renounce absolutely ... the right to use" without, at the same time, renouncing the actual use and the benefits of that use. In other words, renouncing speciesism means renouncing privilege – human privilege. This is why vegans don't consume anything derived wholly or in part from animals or support other practices that contribute to the exploitation of other animals.
A friend pointed out that the Vegan Society and American Vegan Society websites I linked to in my previous post define "vegan," as opposed to "veganism." The Vegan Society answers "What's a vegan?" (as opposed to "What is veganism?"), and the AVS answers "What's is Vegan?" – the 1976 article I quoted yesterday was titled "What is VEGANISM?"
Dropping the "-ism" is problematic; since speciesism is an ideology of oppression that legitimates the existing social order, we need to see veganism as a counter-ideology of liberation for the desired social order.