According to a neo-Marxist worldview, society is stratified into subgroups with varying degrees of social and political power, and the relationships among these groups can be broadly characterized as a dynamic of "oppressors" and "oppressed". Thus, to participate in social structures associated with this stratification, in the progressive gloss, is to perpetuate power imbalances, and thus - to varying degrees - to engage in a form of oppression. This is the basis for the leftist rejection of vocabulary deemed "politically incorrect": using language that actively or passively perpetuates these social structures constitutes a microcosmic instantiation of oppression.
Of course, those who reject the neo-Marxist framework have good reason to reject the notion that "politically incorrect" language is inherently oppressive. Many, reacting to the perceived overreach of leftists, scale up the use of such language in order to make ideological statements. However, in the process the boundary between what is merely "incorrect" and what is crude has been all but erased. While conservatives are justified in denying that "politically incorrect" language is oppressive, the reactionary amplification of the crude can be criticized on several levels.
1) Crude language is not conducive to the pursuit of beauty. In fact, it is inherently contrary to the traditional esteem for "the good, the true, and the beautiful". Speakers like Milo Yiannopoulos argue under the pretense of cherishing virtue, while simultaneously glorifying ugliness in their rhetoric. Pop "anti-SJW" polemics, which rely heavily on slurs, curses, and sexualized language, are a far cry from the eloquence and restraint of past generations of Western thinkers.
2) Crude language is not conducive to sound logic. Instead, it functions as a crutch by those who are either unable or unwilling to take the time to formulate their opinions in a coherent, rational presentation. Sometimes, this unwillingness comes from the perception that the other side is equally unwilling to engage in a rational discussion. However, logic is important not only for discussions with other parties but for the formulation of ideas within a community as well. When an entire community prefers to settle for crude epithets rather than reasonable discourse, this is inherently harmful to the group's intellectual stability.
3) Crude language is not conducive to effective rhetoric. In deliberation - whether it is a formal setting involving two opponents, or just an individual evaluating multiple perspectives - the ability to approach the arguments of the other side fairly and earnestly is absolutely essential. However, the use of crude language creates emotional distance between the speaker and his opponent, making it much more difficult to engage with opposing worldviews without bias.
4) Crude language contributes to the degrading of societal values and standards. Daily, our culture becomes more vulgar, more divided, more sexualized, and less focused on the pursuit of virtue. For one who values virtue to engage in unfiltered crude language is either a paradox, or a sign that the speaker does not truly value virtue.
Of course, there is a place for vulgarity. Yet as the vulgar becomes increasingly intertwined with our politics, our rhetoric, and our lifestyles, it is important to step back and evaluate how the language we use is shaping our humanity.