Why did Iluvatar/Eru give Men mortality?

[The Ninth Valar]

I thought Eru Iluvatar (or is that Illuvatar?) was giving them the ability to experience Arda and then the gift of passing beyond it, to be with him where the music was sung. I have not read the HoM-E so I cannot comment on anything in there. It seems more free will was given to the men, or the pressure of it was greater, since their lives burned quicker. Perhaps that is part of the gift, more of a freedom to choose their course of action and actually see some impact come from it, whereas the elves merely make a wrong choice, live with it for a millenia, then repent after much thought. In the second doom, even Feanor repents when he gives the Silmarils to the Valar. But is that a gift? The elves have the luxury of thinking over their decisions, but is it regret that forces repentence for the Noldor, say, or a sort of mental defeat? Men repenting their ill deeds would be less of a defeat, I think, because they don't have time for regret, because the consequences of their actions are much more immediate and I've lost my train of thought. Perhaps it will come back again.

The elves, it is said, are tied to the earth, they are in a way of the earth, and so long as it endures, so are they tied and must live, either in M-E or Valinor, or in the Halls of Mandos as a spirit or sorts. Remember, they can be reincarnated after a time, and are not truly immortal as they can be killed, simply not by the passing of time but poison or wounds.

Hm. I've rambled, but I think there is an idea present somewhere.