Nikyo and kote gaeshi are two perfectly symmetrical rotations which imply symmetrical effects on uke as one can see of the pictures below.
Nikyo rotates uke's wrist inwards, kote gaeshi rotates it outwards.
Is this the only reason why these two techniques are gathered together in the nikajo category in Tadashi Abe's book?
Yes, but not only.
Let's consider, as we have started since the beginning of these articles, the shomen uchi attack.
As explained in details in Kajo # 6 :
If nykyo omote and kote gaeshi were linked by a similar relation as ikkyo omote and shiho nage, then kote gaeshi would need to be applied in the symmetrical angle of nikyo, ie on the figure:
Is it the case?
Well yes, the direction of the throw is very clear on the two pictures below and one can check that O sensei throws uke in the symmetrical angle of nikyo omote:
Indeed that specificity should not puzzle us for it seems only natural that two perfectly symmetrical movements in terms of process show similarly symmetrical constraints in terms of geometry.
In the same way that ikkyo omote and shiho nage, opposed at 180º in the ikkajo category on the line nº1 (or the first diameter at 60º), nikyo omote and kote gaeshi, equally opposed at 180º create the nikajo category on the line nº2, or the second 60 º diameter.
Without waiting, we can add kote gaeshi on our figure:
Aikido is not a sport, it is a martial art which laws (takemusu) are in harmony with the laws of the universe. Studying them allows the practitioner to understand his place in the universe. Aikido was born in Iwama, O sensei achieved in that village the synthesis of tai jutsu, aiki ken and aiki jo.
The International Takemusu Aikido Federation (ITAF) brings to the practitioner the structure he needs in order to work as close as possible to the reality O sensei MU defined. The official national representations are the guarantee of a teaching faithful to the Founder's.
In modern Aikido, weapons are hardly taught, if taught at all. In O sensei's Aikido, on the contrary, aiki ken, aiki jo and tai jutsu are unified and form together a riai, a family of harmonious techniques stemming from one unique principle. Each techniques helps understand all the others.
Peace is a balance between a human being and the world around him. The true martial art's goal is not to become stronger than one's opponent but to find in that opponent a way to realize harmony. There is no enemy anymore as such, but an opportunity offered to reach unified ki.