The primary advantage of using microservices architecture in software development is its ability to enhance scalability and flexibility. By breaking down applications into small, independent services, development teams can deploy, update, and scale each service independently. This modular approach improves fault isolation, allowing one service's failure to not affect the entire application. Additionally, it enables teams to use different technologies for different services, catering to specific needs. Overall, microservices architecture fosters quicker development cycles and more manageable codebases.