Timeline/context
I got involved in the question because of a flag. To explain the context of the flag, I need to summarise the different posts and comments:
This first answer contained "Your mom has screwed you over".
This second answer contained contained "Your mom didn't screw you over. She just did what she does. She doesn't pay for things unless forced and you enabled it."
The second answer then got two quite highly upvoted comments:
"Your mom didn't screw you over" No... You're right in the fact that "she just did what she does"... which is screwing people over - that's how you get bad credit. This time it was just that the OP ALSO got screwed over.
"She doesn't pay for things unless forced and you enabled it." What the heck is up with this victim blaming? You make it sound like OP willingly put themselves into the situation without knowing the full details
and then the second answer got a "Rude or Abusive" flag, which I was ultimately responding to when I got involved.
Grey areas
In my view, the deleted material falls into multiple grey areas:
Be nice
Firstly, Stack Exchange does have a "be nice" policy. Certainly personal attacks on identifiable SE users are almost always inappropriate. Personal attacks on unidentifiable individuals like in this case are less clear-cut. The first answer's statement was a bit over the line in my opinion. Then the second answer directly criticised the OP which was significantly further over the line.
Irrelevant material
Secondly, the whole debate about being screwed over or not or being enabled or whatever was pretty much irrelevant to the question. Both answers had much more relevant factual statements about the problems of co-signing and how to get out of them. Readers are perfectly capable of drawing their own conclusions about right and wrong anyway. Yes, sometimes it does make sense to give wider advice than the specific original question, but it's another grey area.
Answers that don't actually address the question are always subject to deletion.
I've always understood that to equally applies to specific bits of irrelevant material in an answer where other parts of it do answer the question, though I don't have a specific reference for that right now. But still, to give an extreme example, I wouldn't expect either "Trump is great" or "down with Trump" to survive long if I included it as a single line in an otherwise perfectly good answer.
In this case of course the statements were at least related to the question but certainly wouldn't have survived as standalone answers in their own right.
This isn't a discussion site
The focus of StackExchange is getting answers:
This site is all about getting answers. It's not a discussion forum.
There's no chit-chat.
If someone had actually asked "Did my mom screw me over" that would have been subject to closure as opinion-based.
As with comments, discussions are more likely to get moderated the longer they continue. One or two chatty comments often survive, but if more and more keep appearing then often the whole lot will get removed.
Summary
Overall for me, given the combination of irrelevance, not niceness, and the general back and forth of discussion leading to a "rude and abusive" flag, the logical conclusion was just to remove all that content rather than somehow taking sides by leaving some of it.
We actually get a fair number of flags about answers containing "not nice" content and I generally apply the same test - if it's not directly relevant to the question then removing it as such is the easiest way to deal with it.
Conversely, flags about material which is actually directly relevant to the actual question asked get treated much more skeptically - the answer will typically not get deleted if it's just a bad answer but not rude/abusive etc.
Why is this other content still here?
The fact that things aren't consistently removed across the site is not evidence that we think they are ok, just that moderator's time is limited and usually focused on actual controversies - such as the one I was faced with here given the flag and the comments.
I also thought a bit more about the "your girlfriend is a scammer" example and in general I'd expect those kinds of answers are much more likely to be actually relevant to the question.
Edit wars
Firstly, let me be clear that I was acting with my mod hat on all the way through my interaction with this question - I was applying my judgement as a mod when I edited the answer in the first place, and I explicitly stated that the second time I applied the edit by leaving a comment. Ideally a second mod will also weigh into this discussion but this wasn't a case of me forming a "normal user" personal opinion and then using my mod powers to make it stick.
As far as any conflict between "clearly conflicts with author's intent" and "edits that improve a post" go, in the end it's the job of a mod to resolve that. Joe's answer explains the general approach to mod edits and edit wars so I won't spend time repeating it. From my side, I could have made it clearer earlier that it was an edit for moderation reasons.
What next?
I can see a few possible outcomes:
The status quo at the time of writing is that the first answer has been re-edited with a much milder statement, and the second answer is as edited by me.
Go back to the original content as written by the posters of both the first and second answer.
Go back to the original content as written by the poster of the first answer, but not the second answer.
Put both answers back to how they were after I edited them.
Overall moderation decisions are a judgement call and I'm sure that another mod, or me on a different day, might have made a different one. I don't actually normally spend hours thinking about each decision :-) But now that I have spent a while thinking about it and writing down my instinctive motivations in more detail, I still feel that what I did was a valid moderation choice amongst a range of reasonable options.
As we stand now, I think outcome 1, i.e. the status quo as I write this, is fine and it might be simplest to just leave it at that.
If anyone still wants to push for 2 or 3, i.e. restoring one or both of the stronger statements in the original content, I think another mod should make the call on it. They might want to consider any opinions from mods on other sites, and/or the sample of community opinion demonstrated by the discussion here.