Denied boarding on my flight home. Why won't Alaska Airlines give me a refund?

Denied boarding on my flight home. Why won't Alaska Airlines give me a refund?

I was flying home from Madrid to Seattle on Aer Lingus, booked through Alaska Airlines using miles. But the airline denied me boarding even though I had a ticket. I had to buy a new ticket on another airline, which cost me $3,244. Alaska Airlines wants me to get a statement from Aer Lingus explaining why I was denied boarding. I've spoken to Aer Lingus many times and the airline has assured...