Narcissists Are Competitive
Many people in any kind of relationship with a pathologically narcissistic person find themselves in a competition over everything. Either you can never win, or you are accused of cheating so that you always win. This is confusing and it can be extremely exhausting.
Because narcissists are not capable of regulating their own self-worth and self-esteem, other people are the measuring stick by which they measure their own worth. They either see someone who is better than they are, or someone who is less than they are. This usually depends on how they are feeling about themselves at the time, more than anything else. As with everything, it's all about them and how they are feeling about themselves, rather than the other person or anything that other person has actually done. Remember that other people are mirrors are for the narcissist. Other people reflect all of the narcissist's negative feelings and qualities back to them, causing them to feel shamed and hated. They deny these feelings out of reflex, and as a result they can perceive them as coming from outside themselves, which is why they accuse other people of feeling that way. It's they who feel that way about themselves.
As a result of this constant comparing of themselves to others and using others as a way to measure their own worth, the narcissist is in constant competition with others - and always coming up short. How they react to this depends on the narcissist's personality. Some will accuse others of causing them to fail or holding them back, and others will look for ways they can claim to be better than the other person. Some do both. Some tell lies designed to make them seem on equal footing with the person they feel inferior to. These are all ways of defending against the shame and self-hatred their perceived failures create within them.
For example, if a narcissist is at a party where a relative announces that she is pregnant and the narcissist becomes jealous or feels lacking because she is not pregnant, she may lie and say she is pregnant too. Or she may brag about how great her life is without children, implying - or even saying outright - that people who have children are actually losing out. Depending on the personality, she may even say things like, "Oh, you're pregnant? That's a relief! I thought you were just getting fat!" Or, "I just don't know how people can be so selfish as to bring children into this awful world." This is the narcissist's way of making themselves feel better, and it almost always involves hurting others or somehow making them out to be doing something wrong. They have no way to regulate self-worth or create self-esteem, so the only way they can feel better is by stepping on other people to elevate themselves. They cannot be good unless someone else is bad. They cannot be right unless someone else is wrong.
For the narcissist, even little things are cause for big concern. They can become upset and feel threatened over something as small as someone getting a better parking spot than them or knowing a better route to get to the store. Everything is a competition to pathologically narcissistic people; a competition where, more often than not, they end up the loser and then punish the other person for daring to succeed at something. This is exhausting and unfair. It puts the other person in a position where no matter what they do, they are wrong. If they don't do something or if they let the narcissist do something incorrectly, they will be accused of sabotage. If they correct the narcissist or do something better than the narcissist did or before the narcissist got a chance or whatever, they will be accused of thinking they are better, smarter, faster, whatever, than the narcissist.
Life becomes a series of endless, pointless battles where no matter what you do, you cannot do right. Either you are sabotaging the narcissist and ruining their life, or you are incapable of doing anything right and they are so much better than you. You're doing something wrong regardless. It's important to remember that you are not really the issue, and neither is anything you're doing, more than likely. The problem is that you are dealing with a person that has no self-esteem or self-worth at all who can only prove they matter by using other people's accomplishments - either by dismissing them, claiming them or victimizing themselves with them. It's not your problem.
Dealing with a pathologically narcissistic person is like being involved in a never-ending game where no matter the outcome, in the end you are always the loser. Do yourself a favor: don't play.