Why don't we eat chicken during the nine days?
We don't eat meat during the nine days because meat (red meat) is considered simcha ( joy).
Chicken is considered meat by the rabbis only because they wanted to prevent confusion over eating meat and milk together. Lest someone get confused and say that meat and milk is permissable because chicken and meat is permissable, they put chicken in the same category as meat in regards to the eating of meat and milk together.
However, the aspect of meat that makes it prohibited during the nine days is simcha, a quality that chicken does not posess. Therefore it makes no sense that chicken should be prohibited during the nine days.