I would be frightened too.I'll not venture a guess as to what it is, but I would strongly suggest a second opinion and a biopsy. Hopefully this is something easily remedied.
Men can be real tough. They don't like to admit that something could be really wrong. Maybe it's fear, maybe it's machismo. My DH did the same thing when he was diagnosed with a brain tumor. He decided to just "wait & watch".

I was beside myself! We had 3 kids under the age of 13! After about 3 weeks of me begging, pleading and crying DH finally bit the bullet and had the biopsy. Thank God it wasn't the inoperable cancer the doctor had predicted.
I hope your father will come to his senses and realize that he is scaring his whole family. I don't know if you've had that frank conversation yet, but he needs to hear it.