Conventional Oil may damage your engine?

I took my Chevy Aveo to Valvoline for a simple oil change. The guy said that Chevy recommends a sythetic-based oil. I said "no that's okay, I just want conventional." He said "are you sure?? Conventional oil may cause damage to your engine." Is this actually true? Assuming I get my oil changed on schedule, is it possible for it to damage my engine?