So here's my logic behind why I'm experimenting with identifying as bigender while also not identifying as nonbinary -
I'm a binary trans man who occasionally has days where I have no gender and am agender. When I have gender, it is exclusively binary. When I don't have gender, it isn't binary or nonbinary, it's the lack of gender altogether.
Previously, I felt a kinship with and was drawn to the term bigender. But I did not identify with it for the reason above. Binary trans man + agender isn't two genders, it's one gender and a lack of gender. To me, my agender days are a complete lack of gender altogether, so to conceptualise agender as a gender is a bit odd to me. But I know many people do consider it to be a gender, but this is not how I see it for me.
It has dawned on me though that bigender doesn't have to be literally '2 genders' (the same way bisexuality isn't only attraction to '2 genders' either). But that bigender can also accommodate '2 states of gender' - i.e. I experience 2 states of gender where I experience binary manhood and also the lack of gender altogether. Not at the same time though.
The state of gender where I actually have gender is exclusively binary, so I don't identify with nonbinary. Bigender is usually thought of as under the nonbinary umbrella - but in my case it doesn't.
I've identified with the term genderqueer for a while now as well (which is also often put under the nonbinary umbrella but is actually for any person with queer gender - including cis people!) and my new experimentation with bigender fits neatly under that too. Which I like very much!