An Ammeter if have resistance can make equivalent circuit resistance more than that of the actual circuit resistance. and which in turn reduces the current and hence we face error in the current.
In practical there is no any conductor whose resistance is zero, but practical ammeters have very low resistances which causes very low error and which can be negligible.
But for the ideal or perfect ammeter we need zero resistance so that the property of measuring instrument cannot affect the readings of the circuit.

