I don't know about Japanese laws but does divorce need to be concented by both partners if family hasn't children?
Weirdly kids don't matter that much on divorce in japan, you agree on who keeps the kids like you agree on who keeps the house, there is pretty much no shared parenting and usually, the kids goes with mom, and dad is out of the picture unless they have good relationship with his ex wife( japan is not progressive about this)
well, there are different stages or type of divorce in japan
if both parters agree on the terms, you don't even need a lawyer , that's the method Michi wants to use here, that's why she needs You to sign the papers and use his stamp on the documents, once it's done she will submit the papers to the local city hall, and it's done.
if unable to reach an agreement they can try a mediation, here, you'll need lawyer, and a judge or a mediator will assist parties until they reach an agreeement
you can also use the family court if both partner agree on the divorce but and not okay with the terms
but unfortunalty for Michi, You seems to have no intention at all to sign the papers and is not okay with the divorce in the first place, and unless they find a ''legal reason to divorce' ( could be infidelity, abandonnement by one spouse, domestic violence, but also pretty weird shit like the dissaperance of one spouse for more than 3 years or Serious mental illness of a spouse with no possibility of recovery) well, they stay legaly married ( but after like 10 years, they might agree that '' well, you aren't spouse anymore, so long and thanks for the fish'')
anyway, unless they proved that You cheated ( and that's funny how we get to see the girl You cheated with on this chapter) Michi is pretty much trapped until You make up his mind, and we aaaaaall know how
reliable and adult You is, right ?