Easily. :)))

I think it means that since we all have our flaws (which is completely natural by the way), the insecurity about them drives us to be cynical and critical about the others, just so we might feel better about ourselves, by calling others out on their faults. I'm no Christian, but I really like that story about villagers throwing stones at a woman they thought did something wrong, and Jesus said that if any of them had never done anything wrong in their lives, then go on doing what they're doing, and all of them just stopped immediately. I think it illustrates the point well. 

In one sense it is simply an exercise in logic :  to enjoy finding fault in others is itself a fault, so we must therefore ourselves have faults.

In another sense it is a fairly cynical, but not necessarily untrue, observation of human behaviour.  We distract attention from our own faults by focussing on the faults of others.

It's very stupid and immature in my opinion, not something you would like to live by. 

Basically, hate on others because you hate yourself. But as I said, very stupid and not true at all. Must have been written by a bitter person.