Three accusations in thirty years hardly qualifies as a "regular occurrence." Having spent part of my career in HR, it is not nearly as rare as you would like to think for people (both men and women) to be accused of sexual harassment.

I do meet with women, regularly, just never alone. My refusal to meet alone with women is hardly irrational. It is one of the safest and sanest choices a man can make in the current environment where a mere accusation is often enough to cause the loss of a job and future prospects.

I sincerely hope it never happens to you, but odds are high that it will if you acquire enough power at work. Not a popular view, I know, but still true.