You need to be intimately familiar with your CC&Rs. Chances are that a vote cannot even be taken on something that is not previously noticed to the entire neighborhood. Business itself cannot be conducted at an annual meeting if a quorum is not present. (There are ways of getting around this, such as absentee ballots due at some time after the meeting, however this prevents voting on anything that is not on the ballot.)
I too am my HOA president. Fortunately we don't have anyone complaining about chickens in the neighborhood. I would have to say, though that probably 1/4 to 1/3 have now or have at some time had chickens. Only three of our 8 board members don't have chickens, and one plans to acquire some next winter. Another had some, but is trying to cur down on the number of pets.
Learn a few good phrases such as "thank you for your input/opinion" and "I'll look into that and get back with you."
Do get back with with them, and reference and quote any relevant CC&R provisions, city or county ordinances and/or state law. Be polite, but business-like.
"Dear XXX,
I want to address your concern about poultry in the neighborhood.
City/county code, as set forth in UUU says, "whatever it states."
WWW HOA CC&Rs state in paragraph X on page Y, "blah, blah, blah." Furthermore, the requirement to change their provisions is laid out on page Z, paragraphs A-G, and states, "blah, blah, blah, blah." If you wish to pursue a change to the code, you will need to follow these procedures. However, please be aware that according to state and federal law (you really need to research this to make sure it is correct), changes that remove rights of the members cannot be retroactive. Anyone who currently is in accord with the CC&Rs could not be required to remove their birds."
You might also mention that making rules specifically tailored to one individual is generally illegal.
What state are you located in? How long are your CC&Rs, and are they available online?