Able to be maintained or defended against attack or objection; reasonable or justifiable. A tenable position is one that can withstand scrutiny or criticism.
From French 'tenable' and Latin 'tenere' meaning 'to hold.' The word literally means 'holdable' - something you can grasp and maintain your grip on, which evolved metaphorically to mean a position or argument you can hold onto intellectually.
Think of a medieval castle that's 'tenable' - it can be held against siege. Your argument needs to be like a well-fortified castle: strong enough that you can 'hold' your position when others attack it.
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