IDK, because it is similar to how all types will deal with fear & anxiety like head types or all types may have anger issues like gut types.
It helps to remember that image types are heart types, and it's about personal values or fundamental human emotional/relational needs. Every type arguably has an image that their ego projects and seeks to protect. It helps to remember that image types are heart types, and it's about personal values. So while, say, an 8 may seek to glorify themselves to maintain an image which protects their power, image types actually are really in touch with the core value behind everything. A 2 is in touch with the fundamental need of humans to feel connected and loved and they know were interdependent. When their image is threatened, it is questioning that value and/or that the value is their ultimate motivation. I suppose being an image type, I have a particular empathy for this, as it's not about particular goal so much as upholding a deeper value.
It's not a coincidence to me that most image/heart types have a feeling preference. 2 types are most frequently ExFJs with some ExFPs & occasionally ISFJs. 4s are almost always NFs and sometimes ISFPs. 3s are the only ones who are often Ts, but they are the heart type most out of touch with their heart. They have an issue of untangling objective goals with personal values, but the one value they tend to be very in touch with is independence (opposite of 2 - a truth that we need to have individual achievement and purpose in life), and so they seek to validate themselves through what they do, not directly from people (much more T mentality - tasks/objects above people). Obviously, 4s are in touch with a need for personal significance or having meaning in life.
Competitiveness in an image type is often from a scarcity mindset. It's not that they need to be the best, it's more that they fear that there basically isn't enough love to go around. I suppose the tl;dr explanation is that
the motivation is different - image types are motivated by "heart needs".
I had a feeling you probably talking about enneagram 2s, but I'm glad I waited for you to basically confirm that.
I had thought about that being case, and thought how it typically plays out. Let me know if any of this rings a bell...
2s have a vice of pride. This frustrates their ultimate goal - which is to feel loved, because they fear they aren't lovable and they really hit on a core image type fear - there isn't enough love/meaning/value in the world to go around. It's scarce, and we must be very good or nearly perfect to "win" it, hence the formation of an ideal image that the person feels they must live up to get love or have human value or find meaning.
The 2 pride means they not only build up an image of being really loving, giving, sexy, fun, etc, but they do so to attract love. The problem is, their pride keeps them from accepting the love which puts them in a vicious cycle. They have built up this image of not needing (because of shame over it) and overflowing with virtuous & lovable qualities themselves, and on some level they know that giving to get is not true generosity (that's a crack in their ideal image). But other people can see it. We know what they are doing. And so we want to give them what they need, out of compassion. Here, they may seem to flip the script because they can't accept what they need. Accepting what they need oddly threatens their image - it triggers their pride.
If they are a lower functioning 2, then they can get almost angry if you try to give to them. I have experienced 2s snubbing when you attempt to give to them - they get kind of elitist (I don't need anything from someone like
you) or they become critical in some way. Other times, the 2 rejects what you give because on some level, they know it's giving to their image - they had to "earn" it and it reminds them of that. This is often when they criticize it as "not enough". They also get amnesia over what they received or what others do for others, but they clearly remember everything they did for you & others. This looks like ungratefulness on their part and like they are constantly being critical and judgmental of others (and how reflective of inferior Ti is this? this is probably more specifically ExFJ 2 than simply 2). That definitely leaves you on eggshells and drains people and pushes people away. Then they complain they aren't appreciated.*
When 2s complain about how ungenerous others are, it looks like they want people to be more like them (or how they see/present themselves). So you can adjust to their values...and then they get threatened by you. Because when they were complaining, they were winning. They were at the top. But when you come in and are just as kind or sexy or whatever, now they have to top you! You are threatening them, and they feel threatened because if love is scarce, then they have to compete for it.
I had an ESFP 2 friend who is major one-upper. I almost think she doesn't want you to do too much for her (deep down because she more consciously resents others not giving as much as she thinks she does), because then it raises the bar for what she has to do to be the MOST.
2s often like to give to people who will boost their image more than give back, if they are not very developed. Obviously, healthier 2s learn to accept graciously and genuinely love seeing others give and receive too (because love is no longer seen as a scarce commodity to them).
*This is a side point since sx 2s often don't see themselves as 2s - sx 2s primarily "give" by embodying the fantasy partner of someone else. That's why I throw in words like "sexy" and "fun" along with "giving". They may drop people once they've "seduced" them because they can't deal with a real relationship where they actually accept love from someone. They see themselves as a prize, even as they chase others as their prize. That may become confusing if they intensely pursue people (even friends) and then seem to lose interest once they "get" you (these are most likely to mistype as 7s or 4s, IMO & more likely to be ExFP 2s). I haven't experienced a "flip of the script" with these types, unless it's that they suddenly want you to chase them (?). I suspect the unhealthy ones have an anxious-preoccupied attachment style.
I suspect for an sx 2, suggesting they are an "ordinary type" like an ESFJ is a threat to their image of being seductively appealing. There's a unique factor which will appeal to them, whereas an ESFJ sounds like a mother hen. Unlike 4s, their sense of uniqueness not built on a feeling of defectiveness, but they want to stand out and capture attention. They also may want to be everything to everyone and fit the social romantic ideal. The ENFP prototype is a more romantic image than the ESFJ prototype, and it is associated more with adaptability and spontaneity, things which really appeal to a 2's image (because they feel like this overflowing energy that is whatever people need). Romantic comedies are chock full of ESFJ characters who are the People's ENFP. The female leads have it together and are often super ideal, except they have these little quirks that are supposed to be endearing.
So ENFP comes to represent their ideal image, even if that's not what ENFP actually means. They likely reject the negatives of ENFP because mistyped people tend to do that. No matter how healthy you are, if you are that type, then IMO, you should be able to identify many of the weaknesses in yourself at some point in your life. But as noted above, 2s rarely admit a flaw in themselves other than "I care too much!" or cute stuff like "I lose my keys all the time!".
I have no advice here...this is just what I see going with them. I admit my super evolved coping strategy is usually: "keep people at arm's length".
I do know that for 2s - don't one-up. I let them win and at what they think they want. They stay frustrated, but I can't force them to accept genuine care, and neither will I be forced into some stupid competition.
So in this case, they want to be the Ultimate ENFPs, and I suppose that threatens your identity (?). What is this triggering for you? It's clearly causing some anxiety... understandably.