Natsume's Book of Friends/WMG

Reiko's mother was a kitsune.
As you all know, Kitsune are powerful female (Li'l Kitsune is Special) fox spirits who will sometimes mate with humans when in human form. They are also known to be tricksters, as most foxes are, but are known to keep promises. Now, let's look at Reiko for a moment. Reiko is a young girl who has great spiritual power, and often challenges spirits to duels. She oftentimes uses trickery in order to win them, and has a mischievous personality overall. Those who lose her duels are forced to become her underlings, but she never tries to force the victor to do the same, just as she says. Add this to the fact that she has gold, slit-pupiled eyes, and it's easy to see how this could be possible.

Madara is Reiko's father.
Other youkai often mention Reiko to him and imply that he is only interested in Natsume because of Reiko.

Natsume's father was half youkai.
Seriously, how Reiko came to have a child is never explained, people didn't like her, and she was always alone. How could she have possibly have had a human partner?
 * The fujiwaras, who are from his father's side, do not know about his powers. It's more likely that his mother was the one who saw spirits.
 * Chapter 36 confirms that Reiko is Natsume's grandmother from his mother's side. Also, while Natsume says that he was told that his mother was a rather normal person, the implication is that she was anything but.

Natsume is somehow related to Gackt
Gackt once claimed that he could see spirits, and that his family didn't believe him and began to suspect that he was mentally unstable (Granted, Gackt says a lot of ridiculous things, as the 496-year-old vampire claim demonstrated, but still). An Bishonen that saw dead people/youkai and was considered disturbed because of it? Gee, now why does that sound familiar...?

Natsumes parents were killed by youkai
I'm probably overthinking this but, Matoba said former exorcist clans have trouble with youkai even long after the last person who could see was born into them. Reiko was somebody, who would probably draw the groudge of a lot of youkai to her. Natsume himself is an orphan. It is possible.

Matoba's right eye would have been targeted after he graduated from high school
In fact, there's a picture of him in high school and his right eye is not covered. While this is just bonus material, his right eye also seems to be different (although it could simply be inconsistent art), meaning that he became the clan head after his graduation.

Natsume Reiko lost the ability to see youkai soon after high school.
Whenever we see her in a youkai's flashbacks, she is always wearing her school uniform. It was even stated at some point that many people lose the ability to see youkai when they grow up. Fridge Horror, since if it's true, the same may happen to Natsume Takashi.

Natori is Natsume's amazingly-young-looking grandpa, on his mother's side.
Because not only can he see youkai, but he looks just. Like him. And, he can be very sadistic especially about youkai, just like Reiko. Seriously, he and Reiko would make the perfect match. Whereas Reiko hated most humans, she would probably have gotten along with a powerful (and fabulous) excorsist. He may even know about it, since he seems to have paternal instincts towards Takashi and even offered to adopt him.