Look instead of debating why they used 0.1 or where someone uses 0.05 or even 0.00001! It is better to understand the use of p-values and hypothesis testing in statistics. In layman's terms, 0.1 means that there is a 10% probability that the results are random and not from the drug used.
So yes, 0.05 would be better, even so, 0.00000001. However, further testing is sure to be done and I am sure if someone offered you a drug with a 90% probability that it could help you (in addition to chemotherapy). Must would jump at that! But yet, there is more to review than just the p-value as that is only telling you whether current drug a (chemotherapy alone) is
different to drug b (HER-Vaxx plus chemotherapy).
(20min delay)