Smirnov's line comes at a point in the narrative when he and Popova are immersed in their "battle of the gender" arguments. The entire context of the Smirnov quote is needed to understand the particular section:
Present company always excepted, all women, great or little, are insincere, crooked, backbiters, envious, liars to the marrow of their bones, vain, trivial, merciless, unreasonable, and, as far as this is concerned [taps his forehead] excuse my outspokenness, a sparrow can give ten points to any philosopher in petticoats you like to name!
For Smirnov, the entire notion of women being considered to be social, political, and intellectual equals to men is ludicrous. He considers to them to be petty in nature. In response to the idea that women can develop complex philosophical strands of thought and nuanced analysis, Smirnov suggests women's philosophical insight is comparable to a bird dropping points to women philosophers. Essentially, this is a way of suggesting that women lack the intellectual capacity for formulate complex thought. The reference to a bird "dropping" points of philosophical merit is deliberate in the quote.
Smirnov's characterization as the "boor" or "the bear" is evident here. He is curt and lacks social graces, which he rejects as contrived. He claims to speak his mind (the thing he taps) and sincerely feels that women are not to be considered as intellectual equals to men. The idea of a "philosopher in petticoats" who he thinks might as well gain their insight from "a sparrow" helps to reinforce this dismissive view of women.