[noman-land]

It's all about thinking in thirds. If you want an A chord it has to be A, C, E, in thirds. A major would be A, C#, E not A, Db, E because that breaks the rule of thirds.

Also, and most importantly, if you're playing an instrument like violin, C# and Db are not actually the same note. Since they happen in different contexts, and have different positions in whatever key they're in, they have different psychological roles and are actually played differently by the player.

If I'm not mistaken, a C# would be played slightly sharper, and a Db slightly flatter to fit the particular key.