Why does supporting one group have to mean insulting its "opposite" (see details)?

I do notice it happening. I agree with you that it’s ridiculous. Battling to control your weight because you’re overweight is no more or less stressful than trying to put on weight because you’re too thin. It depends on how the comparison is used. So mental illness is less visible than some physical ailments but no less debilitating. I can see that’s a reasonable assertion. To suggest mental illness is more deserving of empathy is silly.

I don’t know why people do this. I’ll be interested to read other people’s thoughts on this.

You bring up very interesting points that triggers a myriad of thoughts. Good Q!
IMO- On some, often they are ‘push-backs’. Those on one side of the issue may be sick of putting up with the sanctimonious taking pot-shots when they are feel superior. It happens everywhere. The issues where free acceptance is sought, is brought about by taking a stance and not being bullied by groups hell-bent to do so. The desire to not allow some to question the validity or life of another’s self-worth. More power to them!
As far as the joining of the physical vs mental, in each scenario, what are they really pushing when joining the two? What is the bottom-line message? That may help. It may just be statistics that join the numbers together.
One idea: who cares about how, but the cloud that mental health has carried forever, might just have found its way to lose the stigma it has been associated with for centuries. It is a whole new way towards acceptance of an issue, long overdue.
I guess I see these two issues less of a question of feminism, and more towards greater acceptance of others regardless of sex and assigned stigmas.
Neither are particularly sexist. They are about changing the tolerance and awareness about human nature.
Feminism? Let’s talk equal pay. Let’s talk of issues that still haven’t been addressed as far as treatment differentials that were dropped over thirty plus years ago. Femanism needs to go forward concentrating on legalities and rights. Leave care for self-acceptance and effects that concerns both sexes, in another arena.

I’m not totally sure why the impulse arises either, though I could suggest several possible reasons. . . Seconding @msh‘s observation, many of these situations seem to be “push-backs” . . . where one group of people had been shamed, abused, stigmatized, etc., and is then contrasted with an apparently opposing, superior group.

In these cases, the concept of there being a hierarchy (superior/inferior) wasn’t created by the subaltern group, merely appropriated. Once the group gets enough support to enact change, they would want to redefine the way society perceives them. If what a society has presented is a linear ranking of social status, it seems like a natural reaction to try and climb the already socially-recognized ranking rather than branch out into unknown cultural space (even if once established that unknown space could provide level, egalitarian terrain.) It becomes a societal ‘us vs. them.’

I imagine anger could/would also play a role . . . if someone has experienced, or has at least been sensitive to, the disparity of treatment between two groups, they might resent the group who benefitted from the disparity, especially if that group was also causing the disparity. Anger tends to be more divisive than anything, alienating people and crowding out any pangs of empathy that might reach across breach. . . it becomes an emotional ‘us vs. them.’

Perhaps, too, when people are looking for drastic change quickly, they look for the seemingly fastest way to bring the two sides onto the same plane; maybe the thought is that it would be quicker to raise up one side while lowering the other (burning both ends of the rope) than simply trying to raise the one side up to the full height of the other. . . So, a rhetorical ‘us vs. them.’

Or, perhaps those people who support one side by insulting the other do not want reconciliation, for whatever reason. Maybe they feel threatened, maybe they feel hurt, maybe they feel suspicious/uneasy—that the socially superior group will eventually rescind movement towards equality, or that in order to forge that equality, the subaltern group must give up a part of their identity, or simply that the two groups lack trust of each other. A defensive ‘us vs. them.’

Anyway, those are my immediate stabs at the question: societal, emotional, rhetorical, and defensive motivations, that work instead of or in concert with each other. I don’t think that any of them give good support for the practice of insulting the “opposite,” but perhaps they give some reasons why it might happen. . .

I’m with you that it’s frustrating. But then, I’m a feminist who thinks the word “feminism” does mean equality of the sexes. Perhaps if we had a society that put less absolute emphasis on hierarchy, perhaps if we were more dexterous in our navigation of anger, perhaps if we focused more on the post-equal world than on crossing the line, perhaps if we were better able to trust each other, we would feel more able to speak towards a common, multifarious vision?

I think it has to do with the fact that people like labeling and putting other people in boxes. They also dichotomize things so that if they think you’re not in Box 1, then by some illogical deduction, you must be in Box 2 without realizing there are many other boxes, or no boxes at all.

I think it’s simply insensitivity. And perhaps defensiveness. Usually, when people have the double standard pointed out to them, they recognize that they’ve behaved badly. At least, that has been my experience.

I was just thinking about this too, even in relation to having pride in one’s heritage. Why can’t you have pride in your ethnic background or country or what ever without putting down others? Can’t you be proud and humble? Are you so insecure about your heritage that you feel the need to put others down? In every group, I’m sure, there are examples to be very proud about but also examples where the light didn’t shine too well on deeds and historical facts. A balance of pride and humbleness bodes well for any well informed person.

I think @dxs has a good point. People want to see the world in simplified terms so they don’t have to think too hard. I think it is a shame. The only thing that should be binary is our computers, and even if you study that, it is more complex than most people know.

I’m not sure how to phrase this so it doesn’t sound argumentative, because I’m not trying to sound argumentative. . . I guess it’s just, I like to think that people act out of more than a desire for boxes or binaries. I like to think that there are other interlacing factors and complications that go into people’s decisions, and maybe if we could figure those out (in others and ourselves) and address them, we’d find much more common ground than not. . . not sure I’m always good at following through on that sentiment, but it’s what I like to think will help the world. (also: what I wrote above is just speculation, I’m not saying it’s in any way correct or even close. . . I was just trying to think of possible reasons why the apparent boxes/binaries exist/persist . . . ?)

Because for far to many of us support of a group, mindset etc. is a critical part of one’s self identity.

Deriding the opposite reinforces this even more for them.

It’s a fallacy stemming from our more base instincts. If another group is elevated or their portion is increased, then we must be getting less. It might have been true in times of more limited resources, but no so much now. Of course as we over populate and exceed the available resources, this may become true again.

It’s when one group or followers of a group attack the other group either directly or indirectly to give their group a higher perceived weight. Like so many things asked on fluther lately it’s often subtle so people don’t always know it’s happening. It triggers peoples’ tribal instinct and from there it’s on. Whenever there is a dichotomy of one vs the other and you find yourself supporting one or the other I think it’s important to look deeply and harshly at why you support the side you do. I can think of no better example than American politics. Gather a room full of random people, get them to talk about what they believe without identifying political leaning and they will be more or less about on even ground. Drop words like Conservative, liberal, Atheist, feminist, christian, gay and watch the shit fly. Disdain for one group does not always have anything to do with what the group even represents, it’s often how that group’s supporters act. A good example is when supporters of certain groups simply refuse to listen to any criticism even if it is constructive and brush off non-supporters as “pushing back” or “being defensive.” This is like trying to steal the higher ground and it is just a backhanded attack. That is a defense mechanism. Maybe if people would just STFU up and listen to each other every now and then some of this nonsense would go away. Probably would not see people like Trump or Hillary running for office.