Why does inductor exhibits not symmetrical current behavior?
Here's a quick simulation of a classic LR low pass filter fed with an asymmetrical sawtooth wave form: -



Sawtooth rise time is 20 us and fall time is 80 us. Period is 100 us. Note that I just used numbers that were conveneient and I wasn't trying to exactly simulate your circuit. The result is typical of an LR LPF.

This looks just like what you are describing so, if you are still not convinced, please expain what facet of the waveform in your question is not described here.