What is the source for this practice?
There is an elderly Jew with lots of knowledge of tradition that I knew a while back. He came to the Shalom Zachor of my oldest son. There he said the reason for the custom is that Chickpeas were traditionally made with lots of pepper and were very sharp. Beer was served to cut the sharpness of the chickpeas.
I can attest to the sharpness aspect as I have occasionally been served the peppery chickpeas (not the bland American stuff that is popular today) at Shalom Zachors and they are indeed spicy. He was saying that this is the way chickpeas were served more commonly.