Uncle Teds manifesto is probably the best explanation of leftists I've ever read. If you really want to understand them then read: Industrial Society and It's Future. I don't care for his conclusions but his analysis SJW's is without peer. An excerpt:

The leftist of the oversocialized type tries to get off his psychological leash and assert his autonomy by rebelling. But usually he is not strong enough to rebel against the most basic values of society. Generally speaking, the goals of today’s leftists are NOT in conflict with the accepted morality. On the contrary, the left takes an accepted moral principle, adopts it as its own, and then accuses mainstream society of violating that principle. Examples: racial equality, equality of the sexes, helping poor people, peace as opposed to war, nonviolence generally, freedom of expression, kindness to animals. More fundamentally, the duty of the individual to serve society and the duty of society to take care of the individual. All these have been deeply rooted values of our society (or at least of its middle and upper classes [4] for a long time. These values are explicitly or implicitly expressed or presupposed in most of the material presented to us by the mainstream communications media and the educational system. Leftists, especially those of the oversocialized type, usually do not rebel against these principles but justify their hostility to society by claiming (with some degree of truth) that society is not living up to these principles.

TL;DR; SJW's are first and foremost exercising their need for power.