Let me begin by outlining a few basic laws of nature.
Scarcity
Resources are scarce, with scarcity proportional to relative supply and demand.
Ego
People tend to consider themselves better than they really are (and thus deserve better than what they currently have).
Randomness
The universe is stochastic, and unfortunately people like to imagine life is more deterministic than it really is. (Heck, even Einstein refused to believe God will throw dice.)
As a consequence, when people cannot get what they want, they complain about injustice, and question the fairness of the process that allocates the scarce resources.
Unfortunately, none of these will not help or change anything. People will just think you are a whiner. And do not even attempt to ask why you did not get what you want; you are forcing people to either tell you a white lie (e.g. you are really good; it is just that we cannot figure out a good task for you to do right now) or be impolite (e.g. dude, you really have no idea how lousy your performance was?) or to confess they really have no clue (e.g. huh, we cannot really decide between you and another candidate, so we picked the taller one).
Specifically, under a lot of situations, the decision depends on a lot of factors. For example, there is this famous thing called *affirmative action* in the US that discourages discrimination in job and school opportunities. The intention is all good, until people start to enforce hard quotas, like reserving a certain percentage of openings to a certain group of (alleged) minority. Then, if the real application pool does not contain that percentage of qualified minorities, the process will deem to hire a minority with inferior ability than certain more qualified majority. You can say it is not fair, but that is how things work.
Sometimes it can just be random; with hundreds or even thousands of applications for a certain opening, it is just information overload to for anyone to decide who is really good.
My personal suggestion is to stop worrying all of these, and use the rejection or denial as a source of motivation. Prove to the world that they are wrong, and you are the best.
Getting dumped by your ex? Shine yourself to make him/her regret next time you meet.
Getting rejected by a job application? Outperform whoever got hired instead of you.
Did not get permission to your dream school or professor? Publish better research papers than his/her group.
These being said, I really want to tell whoever applied to be my student: thank you all very much, but since I have received hundreds of applications and I can take probably only 2 (or maybe one more if I can muscle with the department), mathematically it is impossible for me to take everyone I like. Evaluating the quality of a student is more art than science, so I rely mostly on my intuition. If you really want to force an answer out of me, the only thing I can say is that my intuition told me that there are better and more suitable candidates than you. But can I prove it? Heck no, and I doubt if anyone can.