What is the cause that angina pectoris is felt in your left arm?
It has mainly to do with the embryonic origin of organs, with the heart being a typically left sided organ, it develops sharing some nerves with the left thorax and left arm.

There is however high variability, typically among patients but also among coronary vessels. For instance, right coronary stenosis may lead to abdominal pain, whereas left circumflex artery stenosis may lead to no pain at all.

References: 

Essentials of Medical Physiology

Cardiac Pain. Anatomic Pathways and Physiologic Mechanisms

Changing Features of Anginal Pain After PTCA Suggest a Stenosis on a Different Artery Rather Than Restenosis