Each of you is right in a way. Time, in physics, does exist as a dimension, just like distance. Time is around for one reason only – to keep the Universe from getting very crowded. If everythng happened at the same time, there would be an overwhelming nubmer of events occuring all at once – much like if there was no distance, everything would be stuffed into a single point. So time is neccessary for proper workings of the world as we know it.
But that doesn’t mean time is linear or absolute – it is subject to changes and bends, just as any other dimension, and relative to the observer.