It does taste bitter and here's why:
You and I are what geneticists refer to as "super tasters". We have the ability to taste certain toxins in food products that other people can't. This is an ability passed to you genetically by your parents.
In Biology classes, students are given a piece of paper with a chemical called PTC on it and determine whether they carry the "super taster" gene or not. Those with the gene taste PTC as horribly bitter, while those without the gene (the majority) taste nothing. Because the toxic chemical in cabbage, broccoli, tobacco, and other foodstuffs resembles PTC, super tasters taste bitterness.
Google "PTC: Genes and Bitter Taste" to learn more.