For a narrative explanation of this source sheet, see There's More to Eating Matzah Than Remembering We Were Slaves by Ayalon Eliach in Ha'aretz, April 21, 2016, available at: http://www.haaretz.com/jewish/the-jewish-thinker/.premium-1.715607
These two passages offer the generally cited explanation for eating matzah and refraining from eating chametz on Passover: It commemorates the hasty exodus from Egypt because the ancient Israelites did not have time for their bread to rise as they were fleeing. There are, however, a few textual difficulties with this being the only, or even the primary, explanation for these eating practices.
God commands the Israelites to eat the Paschal lamb with matzah while they are still in Egypt, before the exodus. They had more than a week after this instruction to prepare and bake regular bread. This instruction, therefore, can't be about commemorating a rush out of Egypt, because nobody had rushed anywhere yet.
This instruction about avoiding chametz and eating matzah on all future Passovers was given while the Israelites were still in Egypt, before the exodus had even occurred. It could not, therefore, have been about commemorating hastily baked bread that had not even been baked yet.
Additionally, Passover is not the only time chametz is replaced with matzah. This happened all year in the Tabernacle/Mishkan:
What do Passover and the Tabernacle/Mishkan have in common?
The Israelites are told that God redeemed them purely out of love, not because they did anything to deserve it. Passover celebrates this redemption and, hence, this unconditional love. God's presence among the Israelites in the Tabernacle/Mishkan is the ultimate goal of this act of divine love:
But what does God's unconditional love have to do with chametz and matzah?
Bread... The first bread was made in Neolithic times, nearly 12,000 years ago, probably of coarsely crushed grain mixed with water, with the resulting dough probably laid on heated stones and baked by covering with hot ashes. The Egyptians apparently discovered that allowing wheat doughs to ferment, thus forming gases, produced a light, expanded loaf, and they also developed baking ovens... Although raised bread originally relied upon spontaneous fermentation, bakers learned to produce fermentation with yeast....
Bread is arguably the most basic food that humans eat. The difference between matzah and chametz is that matzah is flour and water mixed together and cooked immediately; whereas chametz is flour mixed with water that ferments and expands. Matzah is this basic food in its unleavened, unchanged state; whereas chametz is the same food once it has begun to go through a process of change.
Food is the most prominent thing that we intake completely into our bodies. It thus represents full acceptance. Refraining from chametz reminds us that full acceptance is not conditioned on being transformed, on being "leavened" into better people. Rather, matzah -- especially during Passover and in the Tabernacle/Mishkan -- serves as a physical reminder that we are worthy of full acceptance and love even in our "unleavened" state.