From what I understand, the people you're annoyed and confused by are the ones who act like friends, but love to see you fail at something- they seem to get a laugh or some sort of ego-boost from it, as if to say "Look at that! You're so perfect, and YOU fell!"
In gradeschool, these people are a lot easier to spot, and they're actually given a name: Bullies. They're easier to spot because children aren't quite as subtle as adults. They try to MAKE happen what they want, which often means trying to force another child into feeling like they fell, or manipulating them into doing so.
As adults, however, those people have learned and grown; it's not socially acceptable to cause someone else to hurt anymore, and it's also much less satisfying to cause someone else to fall, when they'll just do it themselves, eventually! So, they sit and bide their time, they'll make nice and do pretend, and now that they're adults, they've had a lot of practice at "making nice." By the time they're adults, too, they may have found other bullies to be "friends" with, who all do these things to each other, under the guise of "That's what women do."
The idea of "That's what women do" comes in part from our media (showing women being catty or competitive with each other over things, such as grace, the affection of a man, or beauty), and in part from our social upbringing. Many women learn these behaviours from their Moms, who learned it from their own Moms. They don't have only one role model, they have many, as their Mom would have surrounded herself by others that are like her. We like friends that validate who we are, who we believe we should be, and these people are no different. So, the catty, competitive, but outwardly sweet and friendly behaviour continues.
From my understanding and personal experience, it's about Ego. It's that part of all of us that says "You're not good enough," and it's something that tortures everyone. It's something that drives us all, either to distraction, or to perfectionism, or to whatever else. It's hard to ignore, that fear.
While many people learn to deal with it from a "Go away" perspective, teaching ourselves that we are good enough, or simply moving forward from that voice, regardless as to it's presence, and get our things done... They have learned a different skill. As skill borne of comparison, and one that makes that fear and that frightened Ego feel better- but only for a short period of time. In essence, they're stealing your power from you, stealing good feelings about yourself, and by making you appear "smaller," they make themselves appear "larger," even if they're not all standing around you in the cliche circle, laughing and taunting.
Without comparison between themselves and other people, this behaviour wouldn't be able to exist, though, and that's where I think the greatest defense, and greatest challenge comes from.
Something I've noticed here on SV is that comparison is frowned upon. It's actually taught me a lot! I used to compare myself to everyone else... but, I always used to do it and "come up short," tell myself how horrible and useless and stupid I am, especially in comparison to all the beautiful, smart, strong, and graceful women around me. It made me feel awful, and when I realized this was a place where it was discouraged... I began to look at it.
I no longer compare myself to anyone, as best as I can. It's something so ingrained in our world that it's hard to permanently break the habit, but it's possible to work on it, and possible to not be in thrall to it anymore.
You don't need to compare yourself to those women, and if they compare themselves to you, then that is none of your business! You can discourage it, and by doing so, you may find that they push back, they fight you... but ultimately, you're trying to help them! And, you may succeed with one or two. However, by discouraging comparison, you'll find out who those bullies are, really fast! Their behaviours rely on comparison, so when you start to break it down, you'll find out how they hold the behaviour by how they react to you. Some might dismiss, some might fight, some might totally ignore you from then on. And, some might actually appreciate your effort, they might actually begin to change and see that there's a better way to soothe their hurting selves.
Best ways to get rid of comparison, though? Complements. Things like, when they say "Oh you're so much better at that than I am!" You can turn around and say "I think you're really awesome at this other thing!" No need to compare (no "You're better at this than I am,") just stating that they are great at something, end of story. You can tell them it's not a contest, there's no need to compare. That everyone has their own journies, their own skills, their up's and down's. It's what makes us all beautiful, and amazing, and perfect. It's what makes US!
Anyways this is getting long... sorry ;)