@Hyun-Jin1
I don't know when this happened, as the correspondence you posted has been deleted, but it can take several days for the refund to be processed.
This is what Airbnb CS told me when I asked about timings of a guest's refund: "A refund process takes up to 5 business days , but this is a general fact , as I saw refunds completed in few hours , or even 10-15 business days. It all depends on the Guest's Payment Provider..."
Maybe check with your payment provider to see if a refund has been issued or not and if they are processing it.
If you were entitled to a 50% refund under the cancellation policy on your booking, the host cannot refuse to refund it because Airbnb, not the host, collects the guest's payment and should automatically issue any refund due when there is a cancellation.
With Airbnb CS telling you there is no refund, there may well be some confusion here, e.g. they think you mean a refund for the other 50%...
Or, and I have seen this misunderstanding posted here on the CC before, the guest has paid 50% upfront, so after cancellation, they are not due anything back as they never paid the remaining 50% in the first place and so the slate is clear. You do not get back 50% of the 50%! I hope that makes sense.
As to why the host has blocked you, were you pestering him about the refund? I had a guest who I offered to refund on top of what he was due according to the cancellation policy, ONLY if the nights were rebooked. Although I repeatedly told him that I would let him know if that happened, he kept harassing me about it, which was not cool as my offer was a favour and not something I was obliged to do.