My CTO co-founder said I’m disrespecting & treating him like he is my underling. I’m CEO, so what does he mean by that?

The question seems to answer itself. If you think that having the title of CEO makes it hard to understand why a CTO would complain that you are treating him as an underling, it probably means exactly that. You are thinking of him as an underling, and probably treating him like one too. He finds that disrespectful. It is disrespectful. Founding teams are partnerships. Your title is chief executive officer, not only an executive officer.

In a healthy co-founder relationship, the CEO does not tell their co-founders what to do, and they do not pronounce judgement on their co-founders’ merits or performance. Rather, they work as a coach, visionary, public face, administrator, and head recruiter for the organization, in partnership with others who have different duties, in particular a CTO who leads engineering, and likely product development, testing, and possibly design. Decisions are made by consensus, and differences are settled by persuasion, ideally based on evidence and analysis.

If two co-founders reach an impasse, to the point where a CEO gets the final word because of their position rather than their leadership, I would say that the relationship is broken and you should seriously consider whether you should be in business together (or whether the individual in question is truly a co-founder). For what it’s worth, as an investor, a relationship like this is a big flashing red “do not invest” sign, basically a one-founder company where the founder is having trouble with leadership, collaboration, and communication. As a sometimes founder myself, a CEO with that approach is a “do not join” sign.