If it's delicate and easily broken, like a rare glass vase or the feelings of an overly emotional friend, it's certainly fragile.
Back in the 1500s, fragile implied moral weakness. Then around 1600, its definition broadened to mean “liable to break.” It wasn’t until the 19th century that the word started to mean “frail” and was used to describe people. Today we use it to describe things like spider webs, unstable political systems, and insecure egos. Synonyms include flimsy, vulnerable, and brittle.