What does it say about our priorities when HPV vaccine recommendations for girls and boys are presented so differently?

It says that the people advocating for vaccinating boys realize that initiatives promoting wellbeing for boys will not get much attention or support from the public. People care more about saving tax dollars than they do about the wellbeing of men, particularly young men, and even boys. There are other examples of this type of disparity in health care services, such as the failure in the U.S. to provide domestic violence services for men.

Your questions is a good one because it highlights the fundamental difference in the way the male and female genders are treated in in the western world. For the male gender most people just care about whether the man (or even boy) is meeting his obligations; they care little about whether he is safe, happy or being treated well. For the female gender, the focus on wellbeing, so people care when they see women who is suffering or being mistreated.

Ultimately, these biases find their way into public policy and men are expected to solve their own problems while women's problems are issues of public concern.

It says that we don't give a damn about boys and the throat cancers that men get from HPV - transmitted via oral sex.

Indeed, the throat cancer fatality numbers from HPV are comparable to the cervical cancer fatality numbers from HPV. However, the former victims are "only" men!