What is the purpose of supporting your ideas with textual evidence?

The purpose is so that your claim is stronger if you say "Well I think that all paper should be colored paper" (just an example) well your claim would be stronger with some evidence or facts that other people have created.

Explanation:

Hope this helps!

closer examination, however, finds the mcdonald's kind of job highly uneducational in several ways. far from providing opportunities for entrepreneurship (the lemonade stand) or self- discipline, self-supervision, and self-scheduling (the paper route), most teen jobs these days are highly structured — what social scientists call “highly routinized.”  

true, you still have to have the gumption to get yourself over to the hamburger stand, but once you don the prescribed uniform, your task is spelled out in minute detail.