"O-Sensei would get angry if we practiced in a one-two-three manner. "
I get the impression Osensei really did not want people to steal what he believed he was passing on from the kami
. He at least named sets of movements (ikkyo, nikkyo, sankyo... ichi no tachi, ni no tachi, san no tachi... etc).
That makes it sound like he didn't want people to learn things, which implies that he did not view himself as teaching a martial art. if you are a teacher trying to disseminate or spread something, how could you scold people for practicing?
I don't quite think that's it, but I do wrestle with this concept a lot in my own Aikido life.
I think it is more that Osensei didn't want his art formalized or systematized.
Which has been problematic for Aikidoka within Japanese society and without, but at least leaves us with a lineage of sorts...