"Moved forward" means moved to an earlier time. "Pushed back" means moved to a later time. (The Wednesday meeting has been moved to Monday.) These are idioms, and so you can't figure out what they mean by thinking about what they should mean.
While you can think about moving along the time axis as being forward or backwards, you have to specify which you want; later times does not necessarily mean going forward. For example, when we think about position, moving toward bigger x values might mean going forward or it might mean going backward, depending on which way you face. Since you can't even face towards later times (or any times), I don't think this is a helpful way of thinking of time.