Our Gemara on Amud Beis tells us a reason why the Megillah is not read on Shabbos:

⁦Rav Yosef said that there is another reason the Megilla is not read on Shabbos: Because the eyes of the poor are raised to the reading of the Megilla. The poor await the day on which the Megilla is read, because on that day gifts are distributed to the poor. If the Megilla is read on Shabbos, it will not be possible to distribute gifts to the poor, who will be deeply disappointed. The Gemara notes that this is also taught in a baraisa: Even though the Sages said that the villages advance their reading of the Megilla to the day of assembly, they also collect the gifts for the poor on that day, and they distribute them to the poor on that day.

At first glance, this is certainly an odd formulation, as theoretically the rabbis could easily have decreed providing alms for the poor on Friday or Thursday, despite Megillah reading being on Shabbos.  The answer is likely coming from two psychological principles:  (1) The emotions of the celebration of Purim will inherently cause more generosity.  (2)  The poor will still feel some sense of loss, not being able to receive the payments during the celebration, or perhaps fear that somehow there will be a reduction or avoidance if the Megillah is not read that day. 

The idea that we should not cause a sense of disillusionment, even if possibly there will be no actual loss, is a wonderful sensitivity of Chazal.  As an example, a good friend of mine has the following practice when tipping the waiter at a restaurant.  He always puts the big bills first, so that the waiter not feel a momentary ping, thinking he or she was given a dollar tip.

In a more mystical explanation,  קדושת הלוי קדושת פורים קדושה כה explains that the “impoverished people” in this Gemara are hinting at the physical aspects that must be elevated on Purim. Purim is a holiday that takes the hidden aspects of God within the physical and material world, and via physical almost hedonistic celebration, elevates them. I believe he is suggesting that the reading of the Megillah must be on a weekday that is less spiritual, so as to allow for the enactment of this contract.  Thus, the Gemara is saying that we need to honor the physical In a specific manner on Purim, and if we read it on shabbos, that would disrupt the purpose.