The assumption in the question is wrong. Most Indians would have paid taxes one time or another.
Whenever you make a purchase at a shop, you pay an indirect tax to the government. When you eat at a restaurant you are paying tax. In fact in almost all scenarios you can think of, there is a tax effect that earns revenue for the government.
The areas which have been left off without taxation, has been purposely left off because the benefits of not taxing it is greater or it is a new and upcoming area and therefore under consideration by the government about it’s tax treatment( like crypto currency )
I’m assuming the OP meant Income Tax, may be. If that is the case, in the most simple terms, it is either because they don’t meet the income criterion or because they are evading taxes.