A CTO isn't necessarily a programmer at all. For example, if a company makes software for gene sequencing, their CTO could be a scientist.

And good managers try to hire people who are smarter than they are.

I'll mention what someone told me what a CTO's job is NOT to me. You can disagree

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CTO's should not be developing your app with your developers.

> He can be reviewing the code; or giving ideas to members and helping the organization by giving them direction

Lastly it maybe unhealthy sign for your CTO to be coding with your developers like he is another developer. He has other tasks that need done than just coding