It isn't really a branding problem. "Toxic masculinity" consists of an adjective and a noun - the former modifying the latter and therefore describing a trait which applies to a subset of the latter. It's common English. A "red apple" isn't easy to misunderstand as "all apples are red." A "hot plate" doesn't imply all plates are always hot.
People who misunderstand this phrase refuse to do so even when the proper definition is given to them. It's not simple misunderstanding, as simple misunderstandings can be simply corrected, but willful ignorance. You can argue for hours and explain in excruciating detail that "toxic masculinity" doesn't mean "all masculinity is toxic," providing sources to that end, and at the end of the day people will still stand firm and refuse to accept it.
>As this is mostly a branding problem, I want to say I recently came across the phrase "Man Box"[1]. That might be a better phrase to use?
Case in point. This site describes exactly what toxic masculinity actually is and what it actually means. But we need a "better phrase" because feminists used the other one and therefore it's tainted? Despite the fact that toxic masculinity as a term originated in the men's rights movement and as a concept is hardly alien to male culture? We can have a conversation about the possible negative aspects of male culture and masculine identity, but we just can't say the bad words with the girl cooties on them?
The problem isn't branding, it's men refusing to accept that any concept they consider "feminist" could be rooted in anything but hate and misogyny. Modern male culture needs to mature and move past the victim complex its built around itself and see the common ground it has with feminists.