It's not special. If a funny nose was a non-visible condition, then I would be advocating against mandatory public funny nose databases too. But, that happens to be a visible condition so there's not much we can do to protect those people.
On the other hand, HIV is a non-visible condition which people could choose not to reveal if they don't want. Why should we take away that right, just because people with funny noses don't get the same luxury?
So we have two situations which both might cause harm. We have the situation where there is no mandatory public HIV reporting, which could cause harm in that it potentially allows more transmission of HIV. Then we have the situation where there is mandatory public HIV reporting, which could cause harm in that it could lead to people with HIV being ostracized. Why do you think the latter has more utility than the former? There have already been many good counterarguments in this thread but I will reiterate a few of them:
- Not every person with HIV is negligent, and to target people based on their circumstance rather than their actions could end up punishing more non-negligent individuals than negligent ones.
- People making risky decisions regarding their sexual partners or use of contraception are already not likely to check such a database even if it existed.
- Whereas the risk of transmitting HIV is exclusive to sexual partners, the risks of being publicly identified as HIV positive are far more widespread -- it could impact your career, your social status, etc.
Interestingly, I found this while searching for people killed for having HIV, which was suggested as a real threat by some other person in this thread to counter my point. I looked for "killed HIV" with DuckDuckGo.
OK, I'll give you the benefit of the doubt and assume that individuals in the HIV database wouldn't be ostracized in practice, whether now or at any point in the future. Still, they would have to live in fear of potentially being ostracized. Remember we are talking about potentially innocent, responsible people here who just happen to be HIV positive. Is the utility of making those people live in fear worth the potential of a reduction in HIV infections? Note that you haven't actually proven that such a database would actually reduce HIV infections, either.
But unsubstantiated benefits should? Furthermore I think you should take a sample of how some HIV+ individuals feel about this issue before calling these fears unsubstantiated. I suspect you will find unanimous agreement with what I'm saying.