What are the reasons for white batchs in armfit, back?

Vitiligo. White or light colored areas without any textural changes could be vitiligo, or a loss of melanocycte activity. There are other possible diagnosis such as lichen s lerpsus and morpheme. To accurately diagnose the condition and for proper treatment you should see a dermatologist.
Doctor can evaluate. A skin rash is hard to describe in words. A rash that lasts a long time or keeps recurring needs to be examined by a primary care doctor or a dermatologist (skin doctor). The doctor can treat it and/or do more testing if the cause is uncertain. New whitish spots can be eczema (sensitive skin, itchy, dry patches), t. Versicolor (a fungus), post-inflammatory (result of prior skin irritation), etc...