Thanks for the reply, orgopete. Yeah, it's one of those questions where a more accurate answer would be to list both E1 and SN1 products, so I don't understand why he would specifically asked for one major product. I even took the MIT OpenCourseWare Exam#3 (Spring 2005) and they never asked a question such as this. If the reaction could produce multiple products, they just asked for the reaction mechanism for each product.
I don't think my professor really "gets it." I mean aren't we supposed to step back and look at the bigger picture (the reasons why we are learning all this). From what I understand, the more products (and increased difficulty in controlling the outcome of a reaction) makes a given reaction pathway more inefficient. Therefore, you need to learn how to spot them, so you can avoid them and only use them as a last resort.
Also, he said that EtO- (reagent) in EtOH (solvent) and a primary alkyl halide (substrate) will give a major product that follows an E1 (instead of SN2) mechanism. When we asked him to explain why, he said that EtO- is a strong base and not a good nucleophile (I thought it was both) and that the polar protic solvent makes it act more like a base. These reasons do make sense; however, I could not find any literature on this either and my textbook says only a strong bulky base (i.e. t-BuOK) follows this rule. Has anyone else heard of this?