Interesting discussion. This is good... I think it's important to challenge and question your art.
From what I've been told, Chatan Yara No Kon is an old kata, from the early 1700's. I'm sure that Tokumine No Kon and Chatan Yara No Kon are related... they might be looked at as one being a challenge, and the other a response. I don't know which is the which, or if it even matters.
The Tokumine No Kon in my style has a series of three stepping in, thrusting pokes that are the offensive counterpart movements to the three stepping-back circular parrys that are in Chatan Yara No Kon.
There's another kata called Tenryu No Kon, that has a combination of three in-place thrusting pokes that would be an excellent offensive bunkai for the three parrys that have been the point of discussion. Could be just as simple as that, but I like how this conversation has forced me to look deeper.
I really like what WuXing said in the last post. That's exacly how this combination was described. The succession of circular parrys were like pakua or taichi pushing hands. When learning this kata, we worked with a partner on this.
The kata that I'm currently learning (Hama Higa No Kon) has two series of these parrys as you're walking a quarter circle - just like the pakua pushing hands.
This is great. Now I have a bunch of questions for my sensei.