The White House press office said the event would be open to the "in-house pool," and as you can see, that includes the AP, which is a foundational part of the pool. But the reporter wasn't allowed in. This deepens the dispute between the AP and the WH.
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This WH press drama is sure to be some “Riveting Storytelling for All of America.”
And you are right - space is one thing; picking and choosing is another.
And to be honest, b/c of so many different media organizations, independent journalists, etc.,that can be an issue in some places. (a good thing, though)