There are 21 days between the 17th of Tammuz and 9th of Av.
This number is the same number of days of special holidays (yomim Tovim, Rosh Chodesh, Rosh Hashanah etc...). The first parsha we read in these three weeks of mourning is Parshas Pinchas which contains a detailed description of these very holidays.
What at is the connection between the 3 weeks of mourning and 3 weeks of celebration?
The Zohar says something which we intuitively know: light is most effective when in a dark room. A candle is far more effective at creating light during the night then during the day.
It is difficult to recognize sanctity in the brightness of day. It is difficult to see G-d when all is good in the world.
We live comfortably as Jews in the 21st Century - we are free to worship, to debate, to fight for Israel, to eat kosher and keep shabbos. We attend the best colleges, we are supreme court justices, and win nobel prizes. We can enter almost any profession, run for President, and become CEOs. America has been kind to us over the last 50 years.
Even with all of the terrible terrorist attacks and the discussion in a rise in anti-semitism, we have never lived in a more prosperous and safe time.
The threat is real, but our day-to-day American lives is safe and comfortable. This can make it more difficult to recognize G-d's blessings.
The Chagim and three weeks go hand in hand.
A Jew without joy is not a jew - a Jew without an 'oy' is also not a Jew.
Let's live balanced, thoughtful, G-d-filled lives.