This Halacha was given over by Rabbi Shmuel Pinhasi (Guest Speaker)
There is an apparent contradiction in the Shulhan Arukh (Orah Haim 551). In one place (ibid. 17) Maran teaches that one should refrain from saying the Shehehiyanu blessing for the entire three weeks of Bein HaMesarim. The Vilna Gaon, in his comments to this passage, notes that the Talmud teaches that when a parent dies, the child says baruch dayan ha’emet, and if he stands to receive an inheritance, he also recites Shehehiyanu. We see that a one mourning a parent may say Shehehiyanu. If so, then why is it customary to refrain from saying Shehehiyanu for the entire three weeks!
We must say that there is a difference between the avelut over a parent, and the avelut of the Bein HaMesarim. One who is mourning for a parent may recite the Shehehiyanu blessing, known as the birkat hazman (the blessing over the "time"), since there is nothing inherently problematic with the time. The Three Weeks, however, are a time during which many tragedies have befallen the Jewish people, and therefore it is improper to say the Shehehiyanu blessing, which praises God for bringing us to this "time" (lazman hazeh).
According to this, we can understand another issue. The commentaries point out that during the Sefirat HaOmer, it is prohibited to take a haircut, yet it is permitted to say Shehehiyanu. However, during the Three Week, when it is permitted to take a haircut until the week within with Tisha BeAv falls (Shabua shehal bo), it is prohibited to say Shehehiyanu. How is this possible?
We can now understand that during the Omer, while a great tragedy happened (i.e. the death of the students of Rabbi Akiva), the time itself, the days between Pesah and Shavuot, are not inherently problematic. The three weeks between Shiva Asar BeTamuz and Tisha BeAv, however, are considered to be a time of misfortune for the Jewish people, and therefore, one cannot say "shehehiyanu vekiyemanu vehigianu- lazeman hazeh".