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https://www.circuitlab.com/circuit/cy3ts2zgt828/inductor-test/

the time domain simulation for this simple inductor circuit shows a current curve that is swinging between 0mA and 50mA.

However, I would have expected it to swing between -25mA and +25mA instead.

Did I do something wrong?

You need some resistance in the circuit, say 100 or 1000 ohms or so. With no resistance all you can do is put energy into the magnetic field then move it out to the signal generator and the voltage going negative with forward current does this. With resistance the energy can be converted to heat