Should we eliminate all mosquitoes from the planet?

Made a storify based on a discussion about a new Slate article:

Love work of @billgates but "mosquitoes kill more people than people do" is just wrong

I truly love the work Bil Gates and the Gates Foundation have been doing over the last years.  Absolutely wonderful stuff.  But I have a bone (or perhaps a proboscis) to pick with this latest effort: The Deadliest Animal in the World | Bill Gates.  The article discusses some "facts" about how many people different animals kill.  And it uses this to argue for the need for more attention to be placed on mosquitoes.  I agree with the conclusion.  Mosquitoes are a big deal and need much much much more work and attention.  But the data is just, well, not sound.  Here is the problem I have

1. Many of the animals, including mosquitoes, are on the list are there because of the diseases they transmit.  For example, dogs are there (for rabies), and tsetse flies are there for sleeping sickness.  That is, they do not kill people directly but indirectly because of a disease they transmit.

2. If we follow that logic, which I am fine with, then we need to add a whole lot of deaths to the "human" column.  After all, humans transmit a whole heck of a lot of diseases that kill humans.  One source I found has the following #s

• HIV/AIDS: 1.78 million per year
• Tuberculosis: 1.34 million per year
• Flu: 250-500,000 per year
• HAIs: >100,000
• Syphilis: 100,000
• Measles: 600,000

and many many many more.   The totals are probably greater than 5 million per year that are killed by infectious diseases where it was humans who transmitted the agent to other humans.  Way more than the mosquitoes.  Again, I agree with the conclusion.  We need lots more attention on mosquitoes.  But there seems little doubt to me which animal is most responsible for the spread of deadly pathogens to humans.  And that animal is us.

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UPDATE 5/3