(This graph is sited from an NIH page.)
There are some reasons for this difference. In short, some factors toward causing cancer have been addressed in recent years. They are smoking, drinking, and obesity. And these factors was dominant in men.
Nowadays, however, women are likely to drink alcohol and smoke as much as men. It means campaigns against such harmful behaviors are not effective in women. The cancer rate in both genders seems to reflect the situation.
The Conversation: Why cancer rates are increasing disproportionately in women – and what we can do about it
Smoking is closely relevant to the onset of lung and throat cancer. Drinking is a risk for esophageal cancer. And obesity is likely to be related to prostate and bowel cancers.
On the other hand, cervical cancer is strictly relevant to the infection by human papilloma virus (HPV). In recent years, vaccination to HPV is strongly recommended in developed countries. Cervical cancer is considered to be prevented with early vaccination. It is good news.
In Japan, however, some people are against this policy. They claim that vaccination has a serious side effect. As they opposed to mandated vaccination, the government decided to cancel the policy of necessary vaccination to HPV for young women. I think it is a stupid decision. Indeed, some people are so vulnerable that they experience adverse effects with vaccination. Nonetheless, the risk-benefit ratio suggests we should accept the vaccination. I am afraid that cervical cancer will increase in Japan in spite of reduced risk in other developed countries.