Wearing a mask can’t increase your risk of infection. Unless it blocks 0% of droplets, it can’t possibly have no net improvement. And if they really were that useless, why do we keep getting doctors to wear them?
I feel you should be linking to a study showing that telling people they must wear masks to go out would reduce social distancing. To me, the requirement to wear a mask only reinforces the danger.
Your first claim isn't true. A mask worn with good hygiene practices won't increase your risk. But taking a mask off, touching it, and then doing other things before washing your hands can.
If your mask got infected while wearing it, then you would have gotten infected had you not been wearing it anyways. So even if your poor hand hygiene renders the mask unhelpful, wearing the mask doesn’t overall increase your risk.
I feel you should be linking to a study showing that telling people they must wear masks to go out would reduce social distancing. To me, the requirement to wear a mask only reinforces the danger.