It can happen in ANY argument. You and your friend/spouse/opponent/whatever are discussing or arguing a topic, and suddenly you find that the terms have been redefined, presumably so one of you doesn't have to admit to being wrong. Most people reading this may actually be guilty of this...I know I have in the past.
Here's a recent example of what I'm talking about. In the Catholic Church (since 33 AD) we have been charged with the mission to "go and preach the Gospel to all nations [to all creation/creatures]..." (Mk 16:15-16). We see examples of this in the Epistles of the New Testament. How it looks in the NT, and how it has looked for 2,000 years, is the Church meeting people where they are and bringing them to Truth for the purpose of Christian unity. The Church has used the term "ecumenism" to describe this effort (cf. Catechism of the Catholic Church, paragraphs 816 and 821). "Ecumenism", as it has been explained in the Church anytime it has been mentioned AT ALL, is always defined by this drive for unity without compromising Truth. So uniform is this understanding of ecumenism in the Church, that when efforts of unity are undertaken at the EXPENSE of Truth...when Truth is watered-down to gain some false sign of unity...it is called "false ecumenism" or "indifferentism".
Yet, not more than a day ago, I saw a friend of mine post a brief article titled, "Ecumenism is Synonymous with Religious Indifferentism". Having redefined "ecumenism", he then proceded to show where the Church has condemned "ecumenism" and that "ecumenism" is a false and heretical teaching of Vatican II. His supporting sources for his claim?? All he could point to were writings of Popes that condemned "indifferentism" and other such attitudes that would attempt unity at the expense of Truth (a.k.a. FALSE ecumenism). So, I argued that the Church has never in its 2,000-year history condemned "ecumensim", rather it has condemned the false notion of unity which has been called "false ecumenism" or "indifferentism". I asked the question, several times and in several ways, "Why are you trying to redefine "ecumenism" to make it into "indifferentism"?" I never got an answer, but I think I made my point. He was redefining the term (or blindly accepting someone else's redefinition) and the position he held could only be defended by doing so. Why? I suppose only he knows, and he hasn't answered that question yet. My guess, judging by the source he kept linking to, is that he is simply accepting some other guy's redefinition of terms in an effort to jump on the holier-than-thou bandwagon...but that's just my fallible opinion.
We see this in several arguments theses days: "marriage", "homosexuality", "forgivness", "judging", "sin", "birth control", "Church", "prayer", "worship", "faith", "helping with the dishes"...all receiving a new "definition" in order to support one or the other person's argument. Some of these terms have concrete definitions, others may be more variable. For the more concrete terms, we should stick with what it is, if we really want a reasonable debate. For the variable, the parties arguing should, at the very least, agree on what is to be understood by the term BEFORE they argue about it. Otherwise, we only argue with a wall. Sometimes there may be flexibility in defining a term, other times there is not. Once an understanding is agreed upon, stick with it. If it turns out that you agreed to a definition that you no longer agree with (perhaps after having done some deeper research), then let the other person know and find out if they are willing to start over with that new understanding. But once a definition has been set or agreed upon, do NOT redefine the terms in order to make an argument. You will lose credibility and end up defending a logically inconsistent position. Don't redefine terms to make an argument!