So, everyone's happy to support equal rights for men and women--in your words we can say they're all "empowering women to identify as equal contributors", but they won't identify as feminists because "society views the equality discussion as a danger since it...empowers women to identify as equal contributors".

Are you sure?

People are universally (in that training group anyway) willing to grant the rights themselves but don't accept the word that means "grant those rights"?!

People accepting something that's accepted by almost everyone is going to result in "harassment, hatred, and even life threats" because...why? The label that means the thing they agree with is stinky??

Color me unconvinced. (Unconvinced is maybe a cool-toned gray?)

If you're at another training, maybe instead of declaring to the trainees that they're feminists, you should ask them to share why they say they're not. And really listen.

Maybe they'll say that they've seen shocking levels of misandry be propagated under that label, and they don't want to have anything to do with that.

Maybe they'll say that the label sounds radical and revolutionary but they don't see any need for a revolution because in economically developed countries most of the most important battles have been won and the remainder can be reached gradually.

Maybe they'll say that the label sounds insipid and ineffectual. #ImWithCrispin.

Maybe they'll say that they they think stressing commonality is a better way to achieve equality than stressing a multiplicity of differences via intersectionality. (If they are up on the different waves of feminism.)

Maybe they'll just say that things other than equal rights between the sexes end up attached to the label "feminism" and they don't want to support everything that might get attached to the term. They'd rather just state the position they agree with.

Maybe they'll say that they support equal rights but that equal rights doesn't mean equal conditions and they think "feminism" gets used to mean the latter.

Maybe they'll say that they hear odd phrases like "dismantle systems of oppression" and don't see how that connects to anything in their lives, and don't want to sign on to anything they don't understand.

Maybe they'll say that they hear odd phrases like "dismantle systems of oppression" and they do understand, and think the philosophical traditions that gave us such ideas is epistemologically bankrupt and leads to favoring untestable nebulous conspiracy-like beliefs over focused actionable work to improve equality for women.

Maybe they'll say that they are really committed to equality but find that most people who call themselves feminists seem completely unconcerned when hearing about areas where males have fewer rights or are lacking opportunities.

Maybe they'll say that they don't need to explain themselves when they campaign for the rights of women and girls or humanity as a whole. Everyone gets it. It's a good thing. It doesn't need a label anymore. It's normal. Nobody's an abolitionist any longer because we all agree that slavery is wrong. If someone goes around trumpeting that they're an abolitionist, what's stinky isn't the label...it's that something is seriously wrong given that they think they need to announce it like that.

Maybe they'll just say they don't really know what the word means.

There are a lot of possible reasons to not style oneself a feminist even while supporting equal rights. They might not all be valid reasons, but the first step is to understand the reasons as far as they go.

But I'd be really surprised if you got a lot of people saying stuff like, "You know, I think if I admit that I believe in equal rights, people will ridicule me, then mock me, then hate me, then threaten my life."

So I don't think you've figured out what the problem is with the label. There's broad support (in many places, like your training session) for the core goals. The goals are not the problem. If the label means the goals, that's not likely to be the problem either.

In the very unlikely event that this is the problem: the war was largely won but the label was damaged. No worries! Throw away the label. Pick a new undamaged one that means the same thing, and keep on striving for equality in those places that are still lacking.