The phrase "every dog is a lion at home" means that even the smallest or weakest creature can be brave and confident in their own environment. Synonyms for this phrase include "small but mighty," "a giant in their own world," "a king in their own castle," and "a tiger in their own jungle." These phrases emphasize the idea that every individual has the potential to be powerful and confident in their own setting, no matter their physical stature or abilities. It is important to remember that everyone has strengths and weaknesses, and it is up to each individual to recognize and cultivate their own unique skills and abilities.