Let's dissect your argument:

It is true that much progress is still required for women’s rights. However, to do this, men and women need to work together.

disputable. personally, sounds to me a lot like "slaves and slave owners need to work together to end slavery". no, not really, it's more like "decent people need to work together against evil people". why would men as a collective ever want to overthrow patriarchy that they built and that benefits them?

Because the movement is called “feminism”, it creates the impression that it is a struggle SOLELY for women.

that's because it is.

On the contrary, gender equality concerns everyone.

definitely. doesn't mean it has to make literally everyone's life better.

“Feminism” makes it sound like women fighting for women

correct.

which invokes a defensive reaction in men.

also sadly true.

It is a term that excludes them

yes.

and declares war on them, linguistically.

wrong. what leads you to this conclusion? wanting good things for women has nothing to do with wanting bad things for men, linguistically.

The word represents a side, the women’s side

absolutely.

It makes it sound like the only goal is the glorification of women.

I guess you might interpret it like this.

However, there are no sides in this matter.

that's just, like, your opinion, man.

The feminist movement seeks for the improvemenr of everyone’s life.

wrong. improving men's lives might be a byproduct, focus is and always was on women and women only.

to me, your argument sounds a lot like "how can you make something that is not about men, not including men is literally war". no. it's just not including them. you don't have to be included in every single social movement ever. fighting for people's rights doesn't always have to be fighting for YOUR rights.