Rotator Cuff Injury: This is the most common cause of shoulder pain with a tearing sensation, often resulting from acute trauma or chronic overuse. The rotator cuff is a group of muscles and tendons surrounding the shoulder joint, and injuries to this area can cause significant pain and weakness.

Shoulder Impingement: This condition occurs when the shoulder blade puts pressure on the underlying tissues, including the rotator cuff, when you lift your arm away from your body. It can cause pain and a tearing sensation, especially with overhead activities.
Bursitis: Inflammation of the bursae, fluid-filled sacs that cushion bones, tendons, and muscles near joints, can cause pain and swelling in the shoulder, sometimes feeling like a tearing sensation.
Tendinitis: Inflammation of the tendons, which connect muscles to bones, can cause pain, especially with movement, and may feel like a tearing sensation in the shoulder.

Thoracic Aortic Dissection: Although rare, a tearing sensation in the shoulder can be a referred pain from a thoracic aortic dissection, which is a life-threatening condition requiring immediate medical attention.
Pulmonary Embolism: In some cases, a pulmonary embolism can cause referred pain to the shoulder, which might be described as a tearing sensation. This is a medical emergency.
Myocardial Infarction: Referred pain from a heart attack can sometimes be felt in the shoulder, presenting as a tearing or squeezing sensation.

Suprascapular Neuropathy: Compression or injury to the suprascapular nerve can cause pain and weakness in the shoulder, potentially feeling like a tearing sensation, but this is less common.
Scapulothoracic Bursitis: Inflammation of the bursae between the scapula and the thoracic wall can cause pain in the shoulder region, which might be described as tearing, but this condition is relatively rare.