You learn about ammonia in general chemistry as being only a base. That's because in water, the predominant reaction that occurs is the protonation of ammonia by water to form hydroxide. Water will not, to any significant extent, depronate ammonia. In other chemical environments, however, ammonia can also act as an acid.
In organic chemistry it's time to stop only memorizing definitions and think about reactions logically. Grignard reagents act essentially like SP3 hybridized carbanions with a one minus charge. The anion in the product of the reaction is an SP3 hybridized nitrogen anion with a one minus charge. Other things equal, which do you think is more stable: a carbon anion or a nitrogen anion?