Why i get invert signal when pass through the mosfet
When you apply a decent gate voltage to a MOSFET, it turns on to a low value resistance between drain and source hence, the voltage at the drain becomes very close to the voltage at the source. Given that the source is connected to 0 V, it follows that if you apply a decent gate voltage you will get a drain voltage that is close to 0 V and, when you apply 0 V to the gate, with an appropriate load between drain and positive power rail, the drain will rise to a high voltage that is limited by the power rail.

In other words, a common source configured MOSFET is a voltage inverter.

If you look at your picture in the question, "ON" at the gate signifies current flowing at the load and "off" at the gate signifies that load current is being diverted through the MOSFET and very little will reach the load.

None of that is contradictory.