The last gemara in Makkos tells the famous story of Rabban Gamliel, R' Yehoshua, and R' Elazar ben Azarya who broke out in tears when they saw foxes running in the ruins where the Mikdash had once stood. R' Akiva on the other hand laughed. R' Akiva explained that now that he has witnessed the fulfillment of the prophecy of destruction and sees that G-d's anger has been vented fully on the stones of the Mikdash, he is confident that the prophecy of the rebuilding of Yerushalayim awaits fulfillment.
Why was R' Akiva able to see the silver lining in tragedy where no others could? R' Tzadok haKohen (Pri Tzadik, Devarim) cites the gemara "chacham adif m'navi" (Baba Basra 12) -- wisdom can discern what even prophecy cannot reveal. R' Akiva is portrayed in many places as the exemplar of the ability to derive secrets and halachos of Torah through learning, as opposed to Moshe Rabeinu who received halacha strictly through Divine revelation (Menachos 29).
I would suggest that part of the answer lies also in R' Akiva's background. R' Nissim Gaon (Brachos 28) writes that R' Akiva was a descended of Sisra, the great enemy of the Jewish people defeated by Devorah. The footnotes to the new edition of the Minchas Chinuch, mitzvah #425, cites a variant reading of Gittin 57 from manuscript which identifies one of "the grandchildren of Haman who learned Torah in Bnei Brak" as R' Akiva. Not only did the Jewish people succeed in escaping the danger posed by Sisra and Haman, but these very people who were bent on our destruction gave rise to the personality which led a renewed flourishing of Jewish learning. R' Akiva's very existence is a testimony to the great good that can come out of what appears to be a world of darkness.
In truth, these are not really two seperate answers. A little Shem m'Shmuel: The original plan was for the Jewish people to receive a Torah on 17 Tamuz with everything contained within it. Just as when we read "lo tignovu" we understand the words to mean "Thou shalt not steal" (or kidnap, if you know Rashi), had we received Torah on 17 Tamuz we would have understood from those words every sugya in Bava Kamma right down to every machlokes Ketzos and Nesivos. There would be no intermediary of "interpretation", Torah sheba'al peh, required to tease out extra details -- it would all be clear from the text itself. But because we failed that test, we need a Torah sheb'al peh.
In other words, the original luchos and Torah were for a world where the relationship between G-d's will and our reality is obvious for all to behold. But the sin of the eigel proved that that world does not yet exist. Evil distorts our ability to perceive G-d's plan and his goodness in the world, hiding the Divine intention. Our job is to restore it -- our job is to interpret, to engage in a Torah sheba'al Peh, to dig below the surface of tragedy and heartbreak we see in the world and recognize that there is a Divine guiding hand.
"B'machshakim hoshivani" (Eichah 3) -- zu Talmuda shel Bavel (San 24a). On the one hand, Talmud Bavli, with its intricate sugyos and hairsplitting interpretation, is a result of the darkness of exile which muddled the clarity of Torah. But at the same time, it is that power of interpretation of the Bavli, the ability to see beyond surface meaning and discover greater depths, which can reveal plan, purpose, and goodness where none are superficially apparent.
R' Akiva was the champion of Torah sheba'al Peh because only a soul which was trapped in the darkness of Sisra or Haman and then revealed itself has the power to release the meaning of Torah hidden behind the veil of the smallest tag on top of the smallest letter.
Only a soul like R' Akiva's could teach how to interpret reality correctly so that in what appears superficially to be the bleakest moments we also see through torah sheba'al peh that there is a Divine plan behind everything.
Only a soul like R' Akiva's could look at the ruins of Mikdash and unlock the meaning of destruction as a prelude to a greater geulah.