Trust is important in any field. Think about a salesman selling you a car, a doctor diagnosing your medical condition, a minister preaching a sermon, a teacher educating your children...you see what I mean. Without trust, none of the people in those professions would experience much success. Social workers often have to make or help make life-and-death decisions; without a serious level of trust, those decisions may be compromised.
Social workers must prove themselves trustworthy in order to be most effective. They deal with issues which are personal and often potentially dangerous. Without trust, clients are unlikely to be as forthright or forthcoming about personal matters; without full disclosure, a social worker can not make the best, informed choices about the safety and welfare of those they are supposed to be serving. Trust is crucial to gathering complete, accurate, and pertinent information from people who need it the most.