I heard that ringworm is incurable. Is this true?

No. There are several excellent and safe fungus treatments that should cure this condition.
No. Ringworm is an infection caused by fungus or yeast. It can be treated with a topical antifungal. In some resistant cases not responding to topicals it may be necessary to treat with an oral antifungal. But usually this is a curable condition. It is contagious and spread by contact with infected persons or animals.