That decision is never a testament or rejection of who you are as a person. Law school admissions officers know, and this comes from someone who has read tens of thousands of law school applications, pretty much nothing about who you are as a person—the kindness or reserves of strength that you have deep inside you. There is no standardized test that can measure compassion or motivation.
At face value that might sound like a soothing platitude that someone would say to make another person feel better after a denial, so I am going to say it in real, factual terms. The best employee I know or have ever worked with was denied from Harvard. She went to a top 10 law school with a full scholarship. She was admitted to 8 of the top 14. In other words, she was on paper a strong applicant. But, Harvard didn't see it like that – which is of course their right. Here is the catch. At the time she was also my intern. And because I knew what kind of employee she was, I recruited to her to join my firm full-time. Essentially "I made her an offer she couldn't refuse," to quote The Godfather, by recruiting her and finding the funding to pay someone of her talents. That is her here at the top next to me. Chief Executive Officer means she runs our firm. Which she sincerely should because she is far more talented than I am. At 25 years old she meets with college presidents and provosts and deans of law schools. She talks to the media. She writes data-driven, incredibly powerful research assignments that large organizations and law schools rely on—that they could not produce themselves. She runs the day-to-day operations of our firm. At 25. Imagine what she will be doing at 45? We recently had dinner on a business trip to a law school with my mentor, the global M&A Chair for Gibson Dunn. I asked Jeff if Anna could make it at that BigLaw M&A level and he didn't flinch. Without a doubt she would make it, he said — she would likely surpass his level.
That is one of tens of thousands of examples; it just happens to be one near and dear to my heart. Schools have limited information on you as a person. Admissions officers make good decisions and poor decisions. Just like everyone else. They have good days and bad days. Just like the rest of us. I have podcasted on this here. If your dream school denied you — never forget that you know who you are, they do not.
The loss is theirs, you are going to go on to do great things. Go prove them wrong!
P.S. If you want another example, I was told in the 1st grade I wouldn't amount to anything, which I blogged about here.