I think some people just feel like certain man-made chemicals are either unhealthy, less effective than natural ingredients, or damaging to the environment. Also, some people feel like natural ingredients will be more potent or natural products will be simpler. I can see this especially for people who have allergies to some chemicals. Or fragrances.

I'm not all natural or anything, but I think looking over ingredients is helpful to see what things do well in your hair or what ingredients consistently don't work.
Fine Texture, Normal Porosity, Normal Elasticity. Dyed to brown a few months ago.
Trader Joe's TTT Shampoo
Rinse Out:
Yes to Carrots, AOHR, Aubrey Organics Rosemary Peppermint
LI: Yes to Carrots
Stylers: Shea Moisture Curl Enhancing Smoothie, LA Looks Sports, Suave Professionals Captivating Curls Whipped Mousse