I am aware that Chara's view on crying is not healthy, and telling Asriel that "big kids don't cry" was not right in any way. The plan (and its result) also was not good, to say the least.

Chara killing Flowey, though, does not make them an antagonist. With the player's guidance, they were led to believe that killing the monsters was what should be done. They take control for a moment to kill Sans when Frisk misses again, then kill Flowey because he is in the way. They don't lash out at Flowey (or any other monster) during any route besides Genocide, and only fight at the end due to being guided by whoever is playing.