Isn't it interesting? Extraversion and introversion are one of the more researched personality traits, yet people still have problems deciding whenever they are more extraverted or more introverted.
I guess it adds to the confusion, that in psychology extraversion is comprised from a couple of different concepts: from sociability, to how sensitive somebody is to the outside stimulus, how much is immediate gratification necessary, to how likely the person is to experience the positive emotions.
Yes, before anybody asks, apparently extraverts are more likely to experience positive emotions. They are also more likely to have better social relationships. On the other side they are more likely to be overweight, have financial problems and so on. Just looking over the negative lists for both sides makes me want to not choose either.
Extraversion-introversion axis is also one of the axis that is present in multiple personality types models and traditions, which means that there is a lot of information to absorb to just be able to figure out what it means. And while they more or less describe the similar attitude, their explanations can sometimes be confusing.
That is why, a person can be extravert by one definition and introvert by the other one. I know a case of it, when an ISTP type, so an introverted type (MBTI types) was also a choleric, which is an extraversion type (4 temperaments).
So far the most helpful definition that I have found was that introverted people are the ones that prefer introspecting to acting, but do both. The extraverts are reverse. While they also do both, they prefer acting to introspecting. But even that does not really help. After all, if we do both, how can we know which one do use more?
There is an idea in the Jung psychoanalysis circles that overcomplicates matter even more. In Jung's personality types, the direction of the hero function is the one that decides which one are we. But the direction of the parent function, the one that we use to relate to other people, it opposite of the hero one.
Which is a pretty need idea. It means that we are both extraverted and introverted, but one actually decides our type, and the other is only used when dealing with other people. But this idea, even if it explains the title question (Why people think they are ambiverts), it brings an additional problem.
What do I mean by this problem? Well, most of the situations, that are used to discover the type are social ones. And it is hard to see the differences, since we are likely to be using both of our first two functions anyway. There are differences - I had the pleasure to watch two people which only difference was in the introversion-extraversion part. But I would have put at least one of them in the wrong bin, if not for this interaction.
We could look at particularly which function is used to take care of people - which would tell us that the opposite direction is the primary one. But for that we would need to know people quite well. There are basically two reasons:
First one is that when we simply talk with people, we are much more likely to use the extraverted function to communicate our message, regardless of their strength or place in the stack. Which would give us the overrepresentation in one direction.
The second one is that introverted ways of taking care of people can be quite hidden. After all, introverted ways of taking care of us would be clarifying what we already know about something, making sure that we have the basic comfort and that we continue to move forward, helping us through our hidden feelings or helping us clarify our future. Not really something that gets used a lot when meeting somebody for the first couple of time.
On the other hand, extraverted ways of taking care of people can be a lot more visible and socially accepted. Like making sure everybody in the group feels fine, making sure the outside system works fine, coming up with new ideas for what to do, making us appreciate this moment in life or making us try new food.
Extraversion being more socially acceptable and people pretending to be one does not help the matter much.
So on the end the two forces, that we are both able to be extraverted and introverted and that its use is depended on a lot of factors are the two main reasons why people are confused. Not having good definitions for them just makes the cloudy sky of this concept even worse.