If you really care about his problem you should call for a ban on related research and keep yourself silent. The further we delay the development of such technology, the better. Some people argue it's inevitable; Well it's not. For almost 100 years, despite their huge potential in war, chemical and biological weapons have seen almost zero development because of the strict enforcement of the Geneva convention. Let's keep it that way.
The development of these types of weapons is going to be highly secretive, and not just because of the Geneva convention. Absolutely nothing has gone on in the world in the last 100 years that might tempt the deployment of advanced chemical or biological weapons on any sort of scale. Naturally we haven't seen them used.
I also don't see how burying our head in the sand is going to help on this one. At least compared to nuclear weapons, projects on these weapons could be useful for defensive purposes. Everybody is working more or less within the same confines and rules, and I wouldn't be surprised if relatively similar developments were the result. Even if they aren't, the characterization of these weapons can be used to inform and guide the response plans to try to minimize damage in the case of an attack.
One of the reasons that the nuclear arms race happened, was the "openness" of the competition. You can't hide a nuclear explosion. Your adversary knows how sophisticated you are, and they now have to push 1 step further.
Biological warfare doesn't have to be like this. Be sure that some Darpa or DoD funded secret project is working on countermeasures, but there's another interesting thing: You can stop biological attacks by quarantine. It's very simple, very effective, and doesn't require developing Armageddon-tier weapons in the process. Another issue that's purposefully isn't discussed in the video is how effective the delivery of these weapons are. Simply put, not very. Viruses, the main attack vector, change in every iteration. There's no guarantee you can infect that many people with an intact version of your weapon. Sooner than later, you genocidal weapon will stop being so selective, because it's evolving for it's own benefit, not yours.
And finally, if you really are concerned about this issue, as you should, the right way to fight against it is to find a way to stop the infection and proliferation, to find ways to stop these attacks without accelerating weapons development. There are ways to fight these weapons without building them, and you can definitely do better than starting a public campaign that asks people to develop horrific bioweapons just so we can find a way to stop them later on, maybe.
If you (a nation) are working on this, it's fair to assume your peers are as well. If you have improved on the state of the art, it's safe to assume your peers are in a similar position or will soon be.
By making advancements, all you are doing is proving that other nations with a similar level of technical sophistication can do the same. Even if you make strong assumptions that you are indeed the best, you can't assume other nations will never reach where you are now. Maybe you have 5 years on them, because you are clearly superior? Or maybe you take a more conservative stance and assume you're behind - just in case.
Furthermore, I don't think quarantine would be an effective response to an intentional biological attack. Even just quarantining say, New York City, would be a nearly impossible task. And since this is an attack, why wouldn't all major cities be targeted? There would be no way to contain it physically.
Even if you think pure quarantine is the way to go, there is a lot of useful information that can only be gained by doing the weaponization research. What sort of incubation times could show up? How virulent, etc. Knowing these sorts of things would really improve the quarantine situation. There also isn't really a good way to know without doing the research. It doesn't mean it has to be packaged into a weapon, but the hard part is all done.
So, according to Wikipedia America continued its biological and chemical weapons programs despite signing the Genevea Protocol until Richard Nixon supposedly ended bioweapons in 1969. Additionally, the Federation of American Scientists, founded by members of the Manhattan Project, allege that the US in continuing to illegally develop and research biological weapons in the present day. Of course, the US has continued to practice torture and a variety of human rights abuses in violation of both the US constitution and international law for the past three presidential administrations. The claim that bioweapons are not being actively developed is silly.
Nuclear weapons also follow this - tons of development, but only used once.....so far.