There are things that can be done, especially if the tumor is small and hasn't spread to adjacent organs. I'm not an expert, but in general, solid tumors are
much more easily treated if caught early. Still, "watchful waiting" is a totally valid option for early-staged prostate tumors.
That said, the doctor might be trying to benevolently prevent unnecessary tests, stress, and treatment. Some people hear "cancer" and rush into risky treatments. This is part of the reason the United States Preventative Services Task Force "demoted" asymptomatic PSA screening from "recommended" to "have a talk with your doctor." Their review of the studies didn't show that screening asymptomatic men resulted in a large reduction in mortality. Mostly because prostate cancer is so common and often develops slowly. Somewhat because treatment can bring its own dangers.
At first, in 2012, they recommended against it. Then doctors and patients' groups protested, so now it's "have a talk." We are now starting to see the result of that first decision in the increasing incidence of late-staged prostate cancer.
All this is to say: PSA screening's not a bad idea as long as you can keep perspective if it comes back positive. Out of the major cancer types, prostate cancer has one of the highest 5-year net survival rates [0]. It's over 95% in my state[1].
[0] Net survival tries to exclude the risk of death from other causes. So 100% net survival for a cancer diagnosis means there's no difference from a similar person who didn't have cancer.
[1] The official statistic from the CDC may be lower, but I disagree with some adjustments they make. I believe they force the data to fit their mental model.