Is it wrong to be annoyed when a man who lives with a woman without being married, calls her his wife?

The responsiblities that come with marriage do not come because you stood in front of a preacher, minister, rabbi ect. and said I do. They come with honoring the person who you are with. Many people are legally married and treat their spouses horribly. Are they better then someone who doesn't feel they have to have a piece of paper to be committed to each other.

It's not wrong to be annoyed by anything, but if you live in the USA, you can talk about it all you want but there's nothing you can do about it.

Well, in jurisdictions that recognize common law, they do have the legal esponsibilities that go with it. There seems to be a little undercurrent of resentment in the question, that someone can have all the 'pleasure' of being in a marriage-like situation without any of the unpleasantness that sometimes accompanies it. You can be annoyed all you want - your feelings are no-one's business but your own and there is nothing 'wrong' with them. You can always find people who share your annoyance, and you can always find some who do not share it. In a secular, pluralistic society , as most Western societies are, the state is not allowed to impose a Biblical standard on the marriage contract - if a couple wish to add this extra dimension to their secular marriage, they are, of course, free to do so but that is their own private decision.

Wrong? No.

Right? No.

Annoyances in such matters are merely reactions based on constructs of society, and are therefore beyond the universal realm of right and wrong.

I have heard it said that in some states, one of the ways one may become legally married is to cohabitate while claiming the "significant other" as your spouse.

It might be fun to watch his reaction as you inform him that if he separates from his wife there's a good chance he'll need a divorce lawyer, just because he called her his wife in front of witnesses.

Petty pleasure is pleasure yet, though it reflect harshly on the gleeful.

Certainly you are free to do so, but the rest of us have to wonder why. I don't see how it's any injury to you.

You mention in another comment that you are married yourself. Do you fear that when this man calls her his wife it is somehow insulting to your own marriage? Because I'm sure he doesn't mean it that way. In fact, it is a sign of his own committment to his significant other. Do you worry that this other couple is rejecting the path that you have selected for yourself, and that this somehow speaks badly to the decision you made? This other couple is not married at this time for reasons that have nothing to do with your marriage. There could be entirely practical reasons for this, such as the tax benefits of remaining single, or the wish to keep their assets separate to maintain financial independence or for other business reasons.

Perhaps you are concerned that your relationship is not being held in higher esteem than that of this other couple that is not married. If so, I'm afraid that's not going to be automatically the case in this day and age and you're going to have to get used to it. Most people today react to a relationship based on how they treat each other rather than whether the goverment recognizes their union. While marriage is a nice thing it doesn't always mean that a couple treats each other well, and conversely the absence of marriage vows does not indicate a lack of committment.
Therefore a couple is not automatically better for being married or worse for not being married, but are strong or weak on an individual basis. I would be annoyed about how this man treats the woman he calls his wife, rather than what name he calls her by.

To save yourself the annoyance you could perhaps focus on being grateful that you are legally permitted to marry, which many couples in the world are not.

Well it's your business how you feel about it, but its their business what they do. Their ideas of what constitutes a valid life partnership obviously difer from yours but that doesn't make either of you wrong, and it certainly doesn't give you any right to judge them.
Be annoyed if you must, but keep it to yourself, because the way other people manage their relationships is none of your business. What puts you in a position to judge this? Nothing. Don't imagine that becaus ethey aren't married their relationship is any less valid or succesful than thousands of miserable couples who went through with the wedding.

It isn't anyone's business what someone calls their SO, although that is stupid!

In Texas it's a common-law marriage

Is it any of your business what anyone else does?

I get somewhat annoyed by my fiance's coworkers referring to me as his wife when we're not hitched, but it's not really worth correcting them. As far as whether it's wrong to be annoyed, you can feel however you want to, but there's nothing that can be done about it, nor is it really something worth getting too upset over.

The laws in every state are a little different, but in many places by calling someone,( presenting them to the community) as their spouse, you are considered legally married by commonlaw. Commonlaw marriage is a legal marriage and there is no "commonlaw" divorce.
Ending a commonlaw marriage requires a legal divorce just like any marriage.

I don't necessarily approve of commonlaw marriage, but it is the law. Besides, why should we have to get a "permit" from the government to marry our mate?
This is a contract between two people and their God.
I don't "have a dog in that fight".

I really find it annoying when people who aren't married call each other their wife or husband

It's not wrong, they are living an illegitimate life. They are lying by assuming titles that they have not legally and ceremonially undergone the process of obtaining.

It seems dishonest to me. If he refers to her as his wife, why not be married and treat her as your wife in word and deed. But it's not my problem. If that makes them both happy, fine.

It probably makes the wife feel good but I don't think anyone deserves that title unless they are married. To each their own though. In a lot of states when you live together it is called common law. The state actually considers them married. So guess it depends on where you live.

No, guys do that all the time. Even if he is just casually dating someone, I'll say where's the wife tonight? It's just a phrase. Chill.

that pisses me off. in essence, he is using her as a toy wife, while not giving her the respect of making her his wife for real. he is having his cake and eating it too (so to speak)

I hate when young people refer to each other as husband and wife, that's annoying.