This was made during the first 'arc' of the comic, possibly between pages 11-15.

Original comment from original post on deviantart:
[I suddenly came up with an idea of making special illustrations for my current fan comic, Counterpart, whenever I feel like I want to....
I think it's quite of a brilliant idea for promoting this comic.....right....?

Ahahahahah~~!!!

So yeah, the explanation here is that, we can see that the girls are in quite of a big fight in the comic so far.
And at one part, Blossom mentioned something about how BC doesn't have special powers, which probably offended her so much because it's been 5 years now and all she can do is still just, curl her tongue.
Buttercup, thinking that this was probably the reason why they have so much fights straight away suggested that dangerous bet, while at the same time, thinking that her sisters does not love her for she isn't as special as they are. (I mean, c'mon, the Professor only named her Buttercup because it starts with a B, there was no special meaning to it.)

Being the first child, I, of course, do not understand the feelings of a middle child.

But from what I've read, they're usually the most ignored (stereotypical belief, btw), and BC must've probably felt this. Which later then caused her rough personality.

As she grow older, she gets rougher. Therefore, bringing her even further away from her much softer and graceful sisters.

So, what I'm trying to get at is

the explanation for the words inside this drawing.

Buttercup thought her family does not love her, which is why she kept running away from them, being hostile towards them and such.

When in actuality, they do love her, except they are unable to approach her due to her difference.

So, yeah......

Do you get what I'm trying to say???
]

So....yeah!

Hope you enjoy this piece!