How can testing contribute to higher quality?

Testing's primary contribution to quality is providing information to stakeholders about the quality level of the software. By executing tests and finding defects, testing measures the current state of the product against its requirements. This measurement allows project stakeholders to make informed decisions, such as whether to release the software or to perform more development and testing to improve its quality. Testing identifies where the quality is low, which is the first step toward improving it.

B. Documenting remaining defects is a result of testing, but it's part of the broader activity of measuring and reporting on quality, making option A more fundamental.
C. Testing finds defects, but debugging is the activity that removes the underlying errors (faults) from the code. Testers do not typically fix the software.
D. Testing can identify and help manage risks by finding defects, but it cannot prove the absence of all defects and therefore cannot eliminate all risks.

ISTQB® Certified Tester Foundation Level Syllabus V4.0, Section 1.1.1, What is Testing?: "Testing can also measure the quality of software in terms of defects found, for characteristics such as reliability, security, or performance."

ISTQB® Certified Tester Foundation Level Syllabus V4.0, Section 1.1.2, Testing Objectives: A common objective is "Evaluating a work product to determine whether it satisfies specified requirements," which is a form of measurement.

ISTQB® Certified Tester Foundation Level Syllabus V4.0, Section 1.2.2, Testing and Debugging: "Testing and debugging are different. Executing tests can show failures that are caused by defects in the software. Debugging is the development activity that analyzes and removes the cause of the failure."