I've never heard of a pet bird making the kids sick. I've never heard of a pet bird causing any problems other than making a nonstop racket all day long. From what little information you are giving, I'd say you are overreacting. But, if you could give more details, I might agree with you. (picturing chickens on the kitchen table)
I love pets... I have had birds.... But, I don't think I ever want any more birds because I can't stand the noise.
Some of kid's fondest childhood memories are the pets they had lots of contact with.
http://www.youtube.com/watch?v=p6Hy5HW1y6Y <---this is a bird I'd love to know (but not in my house) I'd totally invite him to my party though.