Suppose one person does not like one word or expression. He would have to use it though, so then he chooses a substitute. The majority of the people however use that word.
Now, since one meaning of a word is the number of utterances in the society, that person consciously and intentionally changes the impact of the word in society. He chooses to do so, even if the impact is very small and perhaps limited to his lifetime.
It is a bit similar to an election where one votes for a candidate who by far will not win. Are there examples of people who do that? Is there a norm that one has or has not the right to choose the word of his like?
Basically every political-correctness movement starts like this. You have a neutral description, e.g., disabled. Then a minority of people starts to dislike this term for some reason (e.g., since it is also used as an insult) and replaces it by some word they consider to be better, e.g., differently abled. This minority has an impact on society, not only popularizing the new term but also moving the public reception of the old term from a neutral to a more negative one. Finally the old term is generally considered to be disrespective and insulting and the new one is considered neutral and preferable. (And then people start all over again.)
In almost every language you will find speakers who oppose loanwords and use neologisms (or existing words) instead. For example, though the vast majority of Germans uses Internet for the internet, there is a small radical minority, which (unsuccessfully) propagates the use of Weltnetz (world network) or similar terms instead. There are also successful examples of replacing a loanword, e.g., some of Phillip von Zesen’s creations.
Yes, there are. As Acattle points out in his/her comment above, some people carefully refrain from swearing, even though the majority of Americans have become comfortable with a little profanity among adults. Common epithets are another class of words that most people use but that some people won't use. There are gentle people who won't use the term "slut" to designate a person known to be promiscuous. Conversely, certain people refuse to use euphemisms in the belief that those who do use them are inauthentic or too timid to speak forthrightly.
However, there are at least two obvious norms that limit to one's ability to refuse to use certain words that most people use. One is that most people expect a speaker to use a variety of language that the listener finds to be grammatically acceptable. An almost certainly hypothetical native English speaker who refused to use "the" might find himself or herself labeled as too eccentric to be worth talking to. The second norm is more important: one must speak in a way that allows one to be understood if communication is one's goal. If our almost certainly hypothetical native English speaker refused to use either the word "person" or any of its synonyms, he or she would have a tough time talking about everyone's favorite subject.
It's common for someone to insist on particular terminology that he considers clearer, especially when he has a point to prove. In fact, it's so common, it's become a storytelling trope. I'll give one set of examples from my native language (English).
The Free Software Foundation publishes a list of numerous English words that it encourages people not to use because it considers them loaded. For example, people say "photoshopped" to mean that a photo is doctored, but FSF encourages use of generic terms (such as "manipulated") so as not to advertise a particular proprietary software product. For the same reason, it discourages "PowerPoint" and "MP3 player". Other examples include use of "piracy" and "theft" to mean infringement, use of "consumer" to mean an individual, describing copyright as "protection", describing a uniform-royalty license offer as "reasonable and non-discriminatory", describing those Linux operating systems that use GNU C Library and GNU Core Utilities as anything other than "GNU/Linux", etc.
In English many rules have been advocated by language purists. They don't like a certain construction, so they invent a rule prohibiting it. Examples: Thou shalt not use "they" in the singular. Thou shalt not end a sentence in a preposition. This is despite the fact that there are numerous examples of well respected authors doing this for hundreds of years, e.g. Shakespeare.
My parents used to avoid the use of "for free", stating that "'free' means 'for nothing', so 'for free' means 'for for nothing'", which they considered made it ungrammatical. I don't know if they still do this. I still prefer to use "free" instead of "for free" although there may be times when I use "for free".