"On their own" can be replaced by several other phrases such as independently, solo, all alone, unaccompanied, self-reliant, self-sufficient, and autonomously. These synonyms imply that an individual is taking charge of themselves or a particular situation without any external assistance or guidance. To be self-reliant or self-sufficient is a crucial skill for personal or professional growth, as it helps in being confident, taking ownership of one's life, and taking calculated risks. In today's fast-paced world, where people are always on the go, it is essential to be autonomous and capable of making smart and informed decisions, being responsible for one's own actions.