Sure, but its exactly because words are important that its called feminism. When you’re talking about “egalitarianism” the goal is so vague that everyone can be on it. That’s why you have names like “feminism”, because that movement is focused on how we live in a patriarchal society and how women have been historically treated unjustly under it. Or “black lives matter”, which, although I’m sure would also agree that “all lives matter”, are focused on why historically, black lives specifically haven’t as much. Same thing for trans rights.
When you combine that all into one, all the nuance of the different groups gets lost and the average becomes “yeah but human rights are so much better than 50 years ago” to shut down discussion.
Its the “LGBTQ+ movement” not the “everyone movement” because it’s calling out how queer people have been historically marginalized and persecuted and not everyone. Cisgender, heterosexual people are the norm, that’s why this subcommunity exists. It just so happens that there are a lot of subgroups within this small community that share very similar idealogies and so it becomes (more or less) one bigger movement.
Moreover, the flag you sent came to be to specifically to call out all the different groups in the umbrella movement, to not let them get drowned out by the vagueness of the combined movement.
All these groups are fighting for different but not necessarily opposing things. Fighting simply for a “better life for all”, while noble, is really naive. You need to get specific about the things you want to tackle.
It’s not like these groups fight alone, you can be a feminist, anti-fascist, queer person of color and support multiple things you believe in.