Why is an ammeter is always connected in series with the circuit?

When considering electricity,

Current (measured in Amps) is often considered the flow of energy.

The force behind the flow is the Volts.

While the volts can be measured between any two points in the circuit (open, or closed), measuring the current, or flow of energy typically requires interrupting the flow.

Somewhat like water. One can measure pressure of the water on a branch, but one must have a way to monitor the actual flow to determine how much water has passed.

There are "exceptions" though.

If you have an AC circuit, then an inductive ammeter can measure the amps around a single leg if the circuit without being installed inline with the circuit.

Even with a DC circuit, it may be desirable to design a bypass or shunt circuit so that the majority of the current bypasses the ammeter, and only a small amount of the current actually flows through the ammeter.