I've been out all day (not in hiding), and can't claim to have all the answers about this. I don't see myself as hysterical, or nasty, or shouty. I am a woman who feels strongly about this topic, however, and women who express strong views are often patronised with those terms.
FWIW, my take on it is that there are three distinct issues running parallel but intertwined (if that's even possible 
).
The first, and in many ways the simplest, is 'ordinary' transpeople, by which I mean people who have chosen, for whatever reason, to live as though they were members of the opposite sex. These people are just like everyone else (ie different from some and similar to others) and pose no threat to anyone. In fact, they are probably at more risk from others than they put anyone else at risk. Most people support their right to live as they choose, and I certainly do.
The second issue is around children and the current fashion for them to 'identify' as one of numerous 'genders'. This aspect of the debate brings up several concerns. The safeguarding issues surrounding the adults who have influence over these children, many of whom have been compelled to (or have bought into) following Stonewall's doctrines about gender, the issue of gender itself, and the medicalisation of 'feelings'.
The third 'strand' is the violence and bullying of the TRAs, which is easy enough to find online. Feminist meetings attached, death threats on Twitter, cancellation of people who speak out and so on. The utter disrespect of men who want to 'redefine the boundaries of womanhood' by remaining genitally intact, keeping beards and so on, but insisting that as transwomen they are women is breathtaking.
Underpinning all of this is the idea that gender and sex are linked. They are separate concepts, although in most societies there are distinct links between them. Sex is biological, and gender is socially constructed. Sex is not about a 'feeling' and is not, in this context, the same as sexuality. Gender conformity is sometimes enforced by law (eg in Afghanistan), but in 'the West' it has been eroded over the past century and longer, largely because of the efforts of feminists who have pushed against it. Women working, men being 'hands-on' parents, the unacceptability of things like strip clubs, men wearing cosmetics, women drinking pints - even women's football becoming mainstream - all these things and many more are examples of gender breaking down. People can pick and mix their lifestyle more now than ever before.
To say that if someone prefers to engage in behaviours that were previously considered to be appropriate for the opposite sex then they must be in the wrong body, or that they are or should become a member of that sex is setting back the cause of feminism by decades and potentially further; and this is where the accusations of patriarchy come in. Linking the notion of 'male' and 'female' gendered behaviour to male and female sex is going to benefit far more men than women, as it would suit many patriarchal men if women wore pretty frocks, cooked and cleaned and were financially dependent on them.
It is Stonewall who brought in the slogan 'No Debate' and simply shouted down anyone who looked for nuance. Many people were (and are) happy for genuine transpeople to live their best lives, and are generally 'kind' people who have no desire to discriminate; but they/we have been decried as TERFs, homophobes (??), and likened to Nazis (???), amongst other things (on here as well as in the wider world), and those doing the shouting are the TRAs.
I will briefly mention autogynephilia here, which is another can of worms. This post is long enough, but the term is easily googled, and is responsible both for a lot of the anti-lesbian feeling of many TRAs, and for the insistence of many transwomen that they can't be told apart from women.
I have probably missed things I will immediately remember, but that probably sums up my thoughts on the matter.
