Tea contains tannic acid - False. Tea does not contain any tannic acid. This myth stems from confusion between tannins (a broad class of compounds) and tannic acid, a specific type of tannin. Tea contains tannins other than tannic acid.
Tannins are bad for you. - False. As explained below, tannins have both positive and negative effects on health, and like most substances, are healthiest in moderation.
Tannins taste bad or make a tea low quality - False. Too high a concentration of tannins in a cup of tea can result in an unpleasantly astringent cup, but tannins also impart a sensation of body and strength to a tea, and make for a richer mouthfeel: a black tea with too few tannins would be more likely to seem watery, weak, or bland.