Kylie, with respect, I would be very suspicious of wherever this information is coming from.

I've only studied anatomy and physiology up the level needed to be a massage therapist. I'm not a doctor, and will stand to be corrected. But the circulatory system flows all around both sides of the body. So there seems to be no logic based in the physiology of the body, that would cause massaging the left side first to make any difference at all.

So I would ask whoever told you this to clarify it with anatomical facts.