Namaste! Good morning, Questor!
The Taoist methods observe the fact that most humans, both male and female, are stronger on the Right Side of the body because the Yang energy naturally moves from left to right, making the right side the active and dominant side. Thus, most people are ‘right handed’. It is even considered ‘unnatural’ in India and the Orient to be ‘left handed’ as this seems contrary to Nature in those cultures traditionally. Yin energy conversely tends to move from right to left, making the Left Side of the body the more receptive, more passive, and weaker side for most folks.
As such, men normally are more Yang than Yin energetically and physically, and are therefore instructed to massage their abdomen 36 times to the right, followed by 24 times to the left. Women are observed normally to be more Yin than Yang, and are therefore instructed to massage their abdomen 36 times to the left, followed by 24 times to the right. In this way, both sexes are able to balance and harmonize the prevailing and dominant energy of their respective constitutions. And like the yogic exercises, all Tai-chi-chuan, Internal Soft Style Kung-fu, and Chi-kung routines begin with a leftward step and/or movement for the same reasons. I see the Internal Arts of both India and China as different in ‘external’ form, but of ‘kindred spirit’ in their ‘internal’ form, so to speak. Modifications of or variations on the same agenda priorities in terms of health and energy dynamics. Both Systems make the same claims for Health, Healing, Life Extension, and Spiritual Self Cultivation! Both have produced Top Level Masters whose Internal Powers are more similar than different. The Yoga exponents tend to apply their training to Health and Spiritual agendas, while the Chinese Masters tend to apply their training to ‘scientific boxing’ agendas, with Health and Spiritual agendas viewed as valuable auxilliary by-products of the training.
Lastly, perhaps your complete avesion to beginning the ‘Sun Salutation’ or ‘Surya Namaskar’ on the left side stems from feeling weaker or less flexible on the left side in so far as the demands of the pose necessitate. If this is the case for you, such impediments are easily resolved by performing more repetitions of the challenging asana on that side, and holding the final position of the pose for a longer time than usual while breathing more slowly and deeply, and relaxing into the asana as much as possible for increased strength and flexibility both. Hope this has been of some small assistance to you!
Light and Love! Hari Om! Aditya