Well, you would be wrong.

As of early April, statistics showed the vaccine breakdown between women and men was generally close to 60% and 40% — women made up 58% of those vaccinated in Alabama and 57% in Florida, for example.

In fact, it's the exact opposite of what you claim.

A few states break the numbers down by age as well as gender, revealing that the male-female difference persists across age groups. In South Carolina, for example, the gender breakdown of vaccine recipients as of April 4 was slightly wider for younger people: 61% of vaccinated people ages 25-34 were women compared with 57% female for age 65 and older.

https://archive.is/88Hdh#selection-664.0-664.1