An ammeter must have a small net resistance to ensure that

An ammeter is always connected in series with the circuit to measure the current flowing through it.

If the ammeter has a significant resistance, it will increase the equivalent resistance of the entire circuit.

According to Ohm's law, $I = \dfrac{V}{R_{eq}}$, an increase in the equivalent resistance will decrease the current in the circuit.

To ensure that the insertion of the ammeter does not significantly alter the original current to be measured, its net resistance must be kept very small (ideally zero).