I've seen that before. At least in my context, this happened because the CEO did not see the CTO as anywhere near equal at all. Instead, the CTO was the CEO's "tech guy". And because he was considered the best or most important tech guy, the CTO got his title.
Sorry about that, but it sounds like you should consider the possibility that the CEO sees you as just another employee (with a fancy job title). In that mental state, it would mean a waste for the CEO to include you into his decisions.
Here I take the blame. I ask from day one to work on some kind of vision. She said that we can't talk for days, so better do it fast.
I said yes (instead doing what I wanted that was to invest the time needed to agree on a vision).
Then I continued saying yes again and again, until without realizing it, I put my self in an employee mindset. Waiting for her to decide what I work as she blocked everything.
I need to move back to founder mindset and start setting some boundaries.
I've been in this situation. The CEO did not listen to his "tech" people about product, marketing or business issues. The company ultimately collapsed, leaving him with 2 options 1) go out of business, 2) fire sale acquisition. Well, he got "acquired" for pennies on the dollar. None of the original investors, himself included, got anything.
I had a job offer recently and it's very obvious that the CEO does way too much CTO stuff than they should. It was my biggest red flag (against everyone's recommendations, since the job offer came with a very generous package)
Sorry about that, but it sounds like you should consider the possibility that the CEO sees you as just another employee (with a fancy job title). In that mental state, it would mean a waste for the CEO to include you into his decisions.