These ideas have been believed for a long time. Research has now shown that these ideas are not factual, while other ideas need more research.
Massage therapy removes toxins
If a person needed help removing toxins from her or his body, that would mean that their liver, kidneys, skin and other organs were failing to do the job they do constantly. If a person's body was not removing toxins itself, massage therapy is not going to help. She or he would need a hospital then, stat! Only the very sick need help removing toxins, it is called dialysis. Here is a link to a video that explains this ancient scam (you will have to cut and paste into your browser to view): https://www.vox.com/2016/9/13/12894190/detox-cleanse-products-scam
Part A - When laying on your stomach on a massage table, eventually your sinus cavities will seem 'stuffed up' or want to run empty. This is not the result of toxin release either. It is the fluid in your sinuses responding to the pressure the massage table puts on your face when lying face down.
Part B - Drinking water after a massage treatment will not help flush toxins. Please see explanation above. Nor will water help prevent sore muscles or increase the benefits of the treatment. If Cynthia offers you water, it is because the air in the massage treatment room is dry and winter is a dry multi-month season in Saskatchewan. She is a kind person.
Massage therapy removes lactic acid
It is now known that lactic acid is actually fuel for muscle, not a by-product of muscle activity. Nor is it responsible for making muscles sore after exercise. The biochemistry of lactic acid is complicated, enough so to avoid explaining it in this format. Instead, try Google Scholar or WebMD.
Massage therapy improves blood circulation
This is a tricky one. What is meant by the vague phrase 'improves circulation'? Improving blood flow to the skin or deeper muscles? Improve circulation throughout the entire body? How long is the effect and is it clinically significant? Research results so far are inconsistent and inconclusive for this idea. If you want to boost your circulation, movement and exercise are the best because it involves the entire body, not just one part of it. Until research about this is specific, beware of vague statements!
Massage therapy helps delayed-onset muscle soreness
The truth is that delayed-onset muscle soreness (DOMS) is not understood. If it is not known why something happens, then how can it be said that something will treat it? Be careful of misguided responses to poorly understood body processes. What is known about DOMS is that it will go away by itself.
Massage therapy will remove or eliminate cellulite
If this were true, Cynthia would have retired rich. Cellulite is subcutaneous fat, or fat under the skin. There is dispute in the medical community as to what causes that dimpling appearance. Is it subcutaneous fat pushing through connective tissue? Or is it the result of how subcutaneous fat is structured and tethered in place? What is known, is that massage therapy cannot smooth out, reduce or eliminate this type of fat. Body fat in general is not well understood by science. Please also know that there isn't a pill, powder, potion or any other kind of additive that will reduce body fat magically. These products do have a slimming effect on one's wallet, though.
Massage therapy will reduce cortisol - a stress hormone
It is well established that massage therapy has beneficial effects on stressed, anxious and depressed people. More research is needed about this, but this effect has nothing to do with reducing cortisol in particular. The reduction in cortisol caused by massage therapy is so small that it is considered statistically insignificant. There are oodles of stress hormones in the body and their physiology is a complicated system. Without writing a book in this space, it is true that massage therapy helps stressed individuals. Likely this is due to the calming effect kind touch has on your skin which in turn soothes your nervous system. There are other factors involved too, one important one which is taking a hour away from stress to take care of yourself.
Massage therapy will help break down adhesions, scars and muscle 'knots'
Muscle 'knots' are areas of higher muscle tone. Muscle tone is controlled by the nervous system. Humans do not have the strength to physically break down 'knots', scars and adhesions. Massage treatment indirectly alters muscle tone because it provides a different stimulus to the nervous system, which in turn, changes muscle tone. It is not the massage therapist's hands or special techniques that brings about changes, it is your own brain.