Your whole basis for calling fire alive is to anthropomorphize it... Sure you can use human terminology for fire and feel it is alive. But then anything can be alive, even a painting, a stain on the wall or a single atom if you like.

Homeostasis is not a sufficient criterion for life and there is a certain quality that is different in entities that fall under the scientific definition(s) of life. Fire isn't even an entity in itself I would argue. Or how would you describe what is part of the fire and what isn't? It cannot evolve on its own either, it follows certain principles and won't evolve new ways to burn.