So … "whatever" first does not mean: "I don't care", although based on some people's reactions, such as a past boss of mine (who happened to be an American-born non-European heritage individual, fully Americanized and educated, but possibly 1st generation, and not yet spiritually liberated — maybe next gen :)), it is clear some people take it to mean that or something similar. One must be judicious in its use for this very reason.
OK, so the real usage is much more benign, and generally friendly way of saying: "I get what you are saying, but your current train of thought appears to be leading in a rather redundant and/or non-productive direction." This is the usage when it is intended to cut off the monologue another is addressing to you, in a friendly manner. It is not intended to end the discussion, but to say let's move on to more productive information.
It is also used to personally cut off your own speech, such as when giving a list of examples, for example: "You could do A, B, C, whatever". i.e. in this sense it is synonymous with "etc".
However, if you want to fast track your understanding of this and other American English modern expressions, the most reliable source is the movie "Clueless", starring Alicia Silverstone, as a California teenager attending an upper middle-class high school. She speaks an advanced form of what used to be called "Valley Girl" speech, which turned out to be so cool and appealing that virtually all of America slowly adopted it one little bit at a time, not too long ago.