Good question. As a “symbol” you're right that pigs are viewed as the most unkosher animal. However, there are many other animals that are equally unkosher according to Jewish law. There are even things "more" unkosher than the pig, such as insects (chocolate covered ants, anyone?).
But you are correct in citing the pig as the most “unkosher” animal. In fact the Talmud often refers to it as “another thing” to avoid calling it by name. Even saying its name is disgusting in Judaism. The Talmud also relates a tragedy that happened on the 17th of Tammuz during the Second Temple that shows this animal’s repulsive nature. During a time of civil war the faction outside the city walls sold animals to the priests inside the Temple for the daily sacrifices and hoisted them over the wall. One day, on the 17th of Tammuz, the outside group upped the stakes of its rebellion and hoisted a pig up the wall instead of a kosher animal — which brought an end to the daily sacrifices (Sota 49).
Why is the pig seen as the most "insidious" of the unkosher animals? It is the only animal known which has a true split hoof like a kosher animal, but does not chew its cud. In this, our Sages saw it as the "worst" of the unkosher, since it "puts on an outer show" of being kosher (split hooves), yet on the inside (chewing its cud, which is a function of digestion) it is "treif !" It therefore symbolizes falsehood, the antithesis of Judaism.
