Moshe Rabbeinu is characterized as the anav mikol adam, most humble man on earth. Thus, it appears audacious and out of character for him to make a declaration asking heaven and earth to listen to him. This is inconsistent with his humility. The Kotzker Rebbe, zl, explains that, indeed, one who is by nature humble does not speak and certainly does not call attention to himself. Therefore, when such an unpretentious person makes a declaration, it is heard. Such an individual who never speaks may posit that he has merited (by being silent thus far) that he should now be listened to.
Indeed, this is a practical concept. No one really listens to someone who lords over him. He is always talking about himself, how much better he is than everyone, his exploits and achievements. They know what he will say, so why bother listening? Let him talk. One who is humble does not speak, does not call attention to himself, never makes demands. Therefore, when he does raise his voice, he garners everyone’s attention. Moshe waited until the end of the Torah, to the end his life, to have his “say.” Interesting, that it was in the form of a shirah, song.