Feminism demands there be a comparable, heritable genetic component that can be traced back through generations as the male Y chromosome can. That’s the political aspect. If mtDNA is not strictly female, then that comes apart. We already had people claiming that the X chromosome is the female chromosome, despite the fact that half of the X chromosomes out there came from the father, not the mother.
Take a look at “fragile X syndrome” for an unhappy view of the effects of inheriting a damaged version of the X chromosome. Call it a feminist disease if you like. With only one X chromosome, affected boys get the worst of it.