Well, doing some googling, I think it's just because when copper reacts with silver nitrate, copper (II) is formed and not copper (I). The reason for this - I don't really know, but it seems that copper (I) is not formed whatever reason.
If you assign oxidation numbers to the atoms in the equation - for a reaction to occur, there must have been a change in oxidation number somewhere (is this correct for all situations?).
If you consider:
Note that the oxidation states don't change and therefore a reaction didn't occur? I don't know if this is the correct reasoning. (couldn't think of a better way of writing them, normally I write oxidation numbers directly above - can't really do this when typing) edit: wait, the oxidation numbers of the silver and copper do change (how did I overlook that...?).But, if you consider this:
There is a change in oxidation numbers and therefore a reaction occurs. Silver has an oxisation number of +1 and there's two atoms of silver. While on the right, they have a charge of 0 (since they are in free elemental form or whatever). You can't have electrons being gained without it coming from somewhere else. These come from the copper. The copper atom loses 2 electrons which are received by the silver.
That's the best way I can explain it (in a way that makes sense to me). I am not entirely sure if what I said about the first situation is correct. There's probably a better way of explaining it.
edit: made a mistake, explanation doesn't work - ignore it.