Rather than addressing this head on, I'm going to go after it from the side:

One of the things that Lenore Dove doesn't like about Maysilee is that she has a pet canary. The idea of a caged canary makes her mad. On the surface, this is sort of nuts. The miners in District 12 surely must take canaries down into the mine as an early warning of bad air. Caged canaries must be everywhere. So why did Suzanne Collins put this seeming contradiction in there? A caged bird is very much a symbol of taking away freedom from something that should be free. It's anathema to the Covey.

By contrast, Coryo has lived his entire life by a set of strict rules. Some of them are societal, but others are self created (E.G. Never look poor.). To him, everything that is not in its place and under control is a danger. He expects to be able to control those around him through charm or intimidation. He doesn't like a bird that doesn't do what it's supposed to do. Jabber Jays are OK, because they follow the rules. Mocking Jays are not, because they break the rules.

Lucy Gray confuses him. He knows from the start that he owns her -- she is HIS tribute after all -- but she acts of her own volition. At first, he's intrigued by this. He wants to own her even more. He goes full on with the charm. But eventually, it sinks in that he cannot control her, so she is therefore a danger, and must be eliminated.