Definition please?

I attended a workshop this past week for my University Studies class as a freshman and it was called Motivation. The motivation seminar basically discussed failure and what it truly means to fail. They asked us what we think failure truly means. People said various things as their definition of failure but the one that stuck out to me was “quitting.” The instructors said that Albert Einstein and many other inventors were not considered failures because even though they took a while to create what they did, they never stopped trying. I completely agree with this because quitting is the only way that one can fail. If you never try, then you will never know. But one young man asked the question, “If failure means quitting then how come when we do not do so well in a math class they say its considered failing and they make us take it over and over again?” Everyone found this question quite amusing but as I looked over at the instructors, they were puzzled as to how to answer the question. I cannot remember what they said but I do remember thinking that people like to put their own definition of things but feel as though they can change it to make it what they want to make it as. I mean I understand some definitions stick like water has the same definition universally. But even lying- some people try to get out of being called a liar even though they clearly lied. We try to find our way out of a lot of things and we like to make certain words apply to us and make other words refrain from entering our minds. It just amazes me how we try to justify our actions and create our own meanings of things that should stick the same. I guess there is no set universal definition for anything if people make their own definition for everything. Right?