For me personally, I'm pretty torn.
On one hand, a lot of people that use the term do have some problematic beliefs. Many look at the "gender" component of intersectionality as "men are privileged/oppressors" and "women are oppressed victims". This is a gross oversimplification and a framing of gender I think is very harmful as well as a gross oversimplification. Many people who are "intersectional feminists" exclude mens/boys issues from their analysis, including many of the leading academic theorists. There is also the issues of "oppression Olympics" that often come from this. The ranking of "oppression" groups and the "but X group has it worse" is often not productive to actual practical social changes or advocacy.
On the other hand, it is a good thing to be inclusive of all of the different social issues that different groups of people may face because of their identity. It is also true that multiple identities overlapping may cause unique issues or additional issues. This is also very true for men. Black men for example are hit hard in that there is a gender discrimination in the criminal justice system and racial discrimination in the criminal justice system. So they are hit with both the gender and racial discrimination and get longer sentencing/more discrimination than any other identity and it causes a lot of unique problems. Lower class/poor men are the vast majority of people who die in the workplace, or who die in war. There are a ton of examples of this that you can get into, lots with LGBT issues too.
A little "test" you can do is if the look at the website everydayfeminsm, which I have been told is a good example of a website that is intersectional feminist, you can look up criminal justice discrimination/gender sentencing gap articles. You will find TONS of articles on the racial component of criminal justice issues, police brutality, police etc. However, you find virtually nothing on the gender sentencing gap, gender discrimination against men, etc. Despite the gender gap being empirically larger than the racial gap.
Whatever the view I think we can agree that male issues need to be advocated for more.
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