Why Not?

Fact #1: The previous Kamuro head, Mukudori and Umineko's father, has already died Fact #2: Mukudori is the eldest child of the main family and possesses the family's kekkai Fact #3: Umineko is the eldest son of the main family and now possesses the family's kekkai

I think the least worst scenario here is that Mukudori is still considered not old enough to take over and someone else (maybe even her mother?) is just keeping the seat warm until then.

Not really expecting that to be the case, though, thanks to this flashback...

These random jerks casually ignoring Mukudori's existence, as if she's simply not in the running. It does seem like the ninja world runs on old rules (arranged marriages, anyone?). It wouldn't be surprising if Mukudori has been snubbed for being female.

Now chapter 84 has thickened the plot both with the confirmation that Mukudori isn't the head and the existence of Fukuro, the female head of the Kuryu family. In the current ninja society, is the Kamuro family behind the times? Is the Kuryu family more open-minded? Is Fukuro just so awesome that she made everyone acknowledge her? Impossible to know at this point.

(I hesitate to use Kasasagi as a data point either way since she was presumably groomed to just be the puppet of the current Uzen head. That and the head trying to strongarm a minor into an arranged marriage. That isn't a man playing by modern rules.)

In addition, for all her bluster, Mukudori is merely a member of Squad 6, she's not the ace of her own single-digit squad like the representative of a great family should be. What this might suggest about her and the Kamuro bloodline in general is a step too far into speculation for this post.

And now, there is a new wrinkle in the matter of Kamuro succession: Umineko. If it's the case that Mukudori has been fighting tradition and prejudice trying to become the head, Umineko proving to be a late bloomer would make everything significantly harder. Because now there is a viable male heir in the main family and there would likely be voices now calling for him to be put in the running as the next head. What Umineko might think about that would again be all but pure speculation at this point.

For the sake of covering all bases, there is also the possibility that Mukudori's already married (possibly arranged/political) and her husband is the current head. That sort of thing can happen to keep a family name going when there are only female offspring. I highly doubt that's the case but since arranged marriages came up with Kasasagi and Yodaka, it's not impossible so it's getting mentioned.