Antiviral chewing gum to reduce influenza and herpes simplex virus transmission

No it's not, it's not science working.

It is either A) underreporting risks or B) not acknowledging risk unknowns and plowing ahead with advice anyway.

This was the major problem and behavior that CAUSED anti-vax opinions. They made safety claims that they couldn't logically make, because they couldn't know. A new vaccine using a new vaccine technology vs a new virus. They did not correctly report the amount of uncertainty and they lost trust. Then folks who "knew better" did their best to manipulate the narriative.

And speaking of manipulating the narrative, you can't use google to find the bits of history that shows the CDC giving contradictory advice because the results aren't there any more. Nearly every result gives the same tone and they're almost all CDC links.

This kind of information control and lack of transparency isn't science, it's power dictating truth.

The actual truth is that the risk of cancers as a result of HPV have a pretty high chance of being prevented if young females get the vaccine, but as you get further away from that group the risk avoided by getting vaccinated gets progressively smaller and runs into the safety uncertainty of taking the vaccine. When you're doing population level risk management you also have to do things like comparing the risk of getting hit by a bus going to the clinic against whatever the clinic could do for you. It is often safer to do nothing than to avoid a very tiny risk because of the very mundane risks you face day to day.

You're missing important stuff here, most notably that recommendations are also based on availability. As the vaccine became more available, more demographics were recommended to take it. Obviously, in the beginning, you want the highest risk groups to take it, then you grow the radius.

They didn't use young girls as some safety experiment. They just had the largest benefit and so, in scarcity, they're prioritized. It's not that scarce anymore.

As an aside, the HPV vaccine also prevents some male cancers, like penile cancer. It also prevents cosmetic, but relatively safe, conditions - like genital and anal warts. That's not the goal of the vaccine so it's not really taken into account. But you, someone who may take the vaccine, should consider it anyway.