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Explanation
The Joke
Two women are having a conversation. One says something provocative, and the other reacts with offense. The first woman explains, "Say you got a son, right? Don't say 'son of a bitch.'" She then points out that the phrase "son of a bitch" is actually far more offensive to the mother than to the son: "That's way more offensive" -- because calling someone a "son of a bitch" is really calling the mother a bitch, not insulting the child at all.
The comic then digs deeper into the etymology. The woman explains that historically, insults directed at men were often really insults to the women in their lives -- their mothers, wives, or daughters. She argues that the target of the swear word is misplaced. The final panel delivers the punchline: "So you're telling me not to say 'your mom is a dog,' and instead say 'your mom gave birth to you in the most unpleasant, unsanitary way' -- with a 'boot full of gallons, heaps of warm clumps?'" The conversation has devolved into something far more graphic and offensive than the original insult, in the name of being more linguistically precise.
The Humor
The comic takes a common, mildly offensive phrase and subjects it to rigorous logical and etymological analysis, only to arrive at something far worse. The humor lies in the academic deconstruction of profanity: by trying to make the insult more "accurate" and "fair," the characters end up with something spectacularly more vulgar and disturbing than the original. It satirizes the tendency to overthink language and political correctness, showing that sometimes the sanitized or "corrected" version of something is actually much worse than what it replaced.