I think for most of us, there are two issues.
The first issue is the forcible redefinition of womanhood to include people of the male biological sex. I think most of us agree that people should be allowed to wear what they want and present how they like without being subjected to abuse, harassment or discrimination. But when it comes to people expecting to be allowed to be in spaces for members of the opposite sex, or compete in their sporting categories, the reality is that this can only be accommodated by trampling over the rights, safety and dignity of those already in that group.
Do you think male rapists who identify as transgender should be housed in women's prisons, thus endangering the safety and dignity of female prisoners, most of whom are extremely vulnerable?
Do you think male bodied people who identify as transgender should be allowed to participate in group therapy sessions for female rape survivors, even though some of those female survivors will find their presence traumatic and be unable to use the service as a result?
Do you think male bodied people who identify as transgender should be allowed to use women's communal showers and changing rooms, even though this means Muslim women will no longer be able to use them?
Do you think male bodied athletes who identify as transgender should be allowed to compete in women's sporting categories, even though this will deprive female athletes who have trained hard of opportunities to compete, medals and prize money?
If you have a problem with these things, you are now considered transphobic. We are expected to put the wishes of all these people above our own rights and needs.
And then there's the word "woman" itself. If the word "woman" must now include male born people, we no longer even have vocabulary to identify and discuss our own sex.
People can identify however they want (even if I don't fully understand what they think they are identifying with). But when their identity includes me, and the fact that their identity includes me prevents me from identifying myself in a way that excludes them even though I don't consider that we share any kind of identity, that's a problem for me and I find it wholly unreasonable.
The second issue many of us have is the medical transitioning of children and young people, particularly girls. There has been a huge explosion of girls and young women wanting to take testosterone and have mastectomies to make themselves appear male. The effects of these hormones and surgery are permanent and irreversible. We think society should be asking why so many girls suddenly don't want to be women, rather than simply affirming their belief that they identify as men.