Students who have spent many years learning English with vocabulary and grammar exercises in their home countries sometimes have a hard time speaking when they arrive in the United States. This is especially the case if the major focus of their studies has been accuracy. They hesitate to say anything for fear of it getting it wrong. Such students need training in fluency. They need to practice talking and writing without stopping to correct themselves all the time. Yes, accuracy matters, but not at the cost of not being able to speak in the first place.
Students who have spent many years in the United States without formal training in English frequently experience the opposite problem. They can speak fluently, that is, they can say whatever is on their minds. But often they make mistakes. These mistakes probably did not matter at first, but the student finds that now they do, especially in a professional context. Such students need to study grammar and practice speaking and writing accurately.
Balancing fluency and accuracy is a tricky business though. Students emphasizing fluency still need to keep grammar in mind, and students improving their accuracy dare not become so concerned about accuracy that they can no longer speak easily. The trick is to find a healthy balance, and that balance will be different for each student.