It seems like this time would be a time of singing and dancing as we count to shavuot. Why does the mourning of Rabbi Akiva's students trump the celebration of the coming shavuot holiday?
Rabbi Akiva himself already informed us that The Great Rule is: Love your fellow Jew like yourself.
This follows Hillel's statement (some 10 generations earlier) that the entire Torah is based on don't do unto others what you don't appreciate being done to yourself and the rest are details.
Since we know that the 2nd Temple was destroyed because of baseless hatred between us - and it hasn't been rebuilt, we can infer that we still suffer from this deficiency.
That means that we're lacking the foundation of our faith: Loving each other unconditionally.
So how can we get ready for Shavuoth? We're missing the entire point of the Torah!
So we shift the focus from celebrating the upcoming festival to mourning those great students of a greater teacher as a constant reminder that we need to work on the foundation - love - before we start celebrating the actual giving of the Torah.
Over the ages we've noticed that this period seem to have a higher incident of antisemitism and the Rabbis - around the time of the Crusaders, IIRC, decided it was time to shift the focus.