Why Fajr?
The day begins in the presence of Allah, before it belongs to anyone else.
Fajr is prayed in the quiet before the world makes its demands. Waking for it is a daily act of sincerity, because almost no one sees it.
It is also the hardest prayer for most people, which is precisely why it carries so much weight in the narrations.
Qur'an
"…and [recite] the Qur'an at dawn. Indeed, the recitation at dawn is ever witnessed."
Qur'an 17:78
Authentic (sahih) hadith
"Whoever prays the dawn prayer is under the protection of Allah."
Sahih Muslim 657