Re-reading all the OP's posts, I don't think the OP knows the reason for the exclusion, because the party host doesn't have any particular reason for excluding the 3.
I'm completely convinced now that OP is party organiser's friend and thinks party organiser is out of order for not inviting the 3. And party organiser has the view that her kid should be able to invite/not invite whoever she wants. OP has probably said, 'not inviting them will send a message' and party organiser has said 'oh no it won't' ('oh yes it will!', 'oh no it won't'). Also I bet the party organiser has excused it by saying 'they won't realise they're the only ones not invited, not everyone who's invited will come anyway, so what's the difference?' and OP disagrees, saying that kids are old enough to discuss stuff amongst themselves.
Thus OP started thread to prove to herself and/or friend that leaving out a few children, even if there is no particular reason for it, no fights, no racism, no falling out, no disabilities, no bullying, no dislike of parents, no class/money issues, no reciprocal party shit....even when there's no particular reason, leaving out just a few kids when rest of class is invited, sends a message.
On that point, I suppose I agree it does send a message, but how the excluded kids and their parents interpret that message is up for some discussion.
And as we've seen with a lot of responses, it can be quite hurtful to be on the receiving end of this type of thing, assuming the 3 are aware that they are the only 3 who weren't invited.
Now for fuck's sake OP, just come back and tell me I'm right about this so I can disappear from MN for several months again!