Antonyms for the phrase "puts down roots" include "uproot," "pullout," "dislodge," "displace," "deport," "evict," "remove," and "transplant." These terms convey the opposite meaning of establishing oneself firmly in a particular place or community. They suggest the act of tearing oneself away from one's current location, rather than settling in permanently. While putting down roots implies a sense of stability and connection, these antonyms imply a sense of transience and detachment. Thus, they speak to the importance of mobility and flexibility, as well as the need to adapt to changing circumstances in one's life.