Some languages have future markers that are banned from or dispreferred in negative contexts. This results in situations of asymmetry in which certain grammatical distinctions made in the affirmative are unavailable in the negative. We propose a diachronic explanation for such asymmetries: future markers first grammaticalize in affirmative contexts and only later, if at all, spread to negative contexts, sometimes with a time lag of hundreds of years. During the period where a novel future marker occurs in the affirmative but is incompatible with negation, the synchronic situation is perforce one of asymmetry. We further argue that newly grammaticalized future markers tend to be banned from negative contexts due to their semantics and discourse function. New futures are typically immediate futures. We suggest that speakers conventionally use novel immediate futures to make their statements more informative. As a consequence, these future markers require the assertion to be stronger than its alternatives. In affirmative contexts, the use of an immediate future gives rise to a strong assertion. On the other hand, in negative contexts, the use of an immediate future leads to a weak assertion, which conflicts with the conventional discourse function of these markers. As a result, novel immediate futures tend to be restricted to affirmative contexts, i.e., they are positive polarity items.