I think it is worth unpacking Gleeson's arguments, because she exemplifies such a common viewpoint among left-ish feminist women.
First: The declaration transwomen are women, transmen are men, trans rights are human rights, followed by: I find it deeply distressing that this targets a group who we all know have a higher incidence of violence and suicide.
The second sentence is supposed to provide justification for the prior claim. But why? Even if it were true that trans-identified people suffer disproportionate levels of violence (they don't) and higher rates of suicide (unclear), it wouldn't make their claims to be the opposite sex any more true.
So what's going on here? What is the argument that is really being made behind the slogan-chanting? I think it is a moral argument that we should all behave as if people can be the opposite sex, because of the deep distress they feel when reminded of their actual sex.
Same for the trans rights are human rights bit. There is no human right to be treated as a sex which you are not. We are back to the argument that it is unspeakably cruel - a human rights breach, even - to remind people of their sex if they claim transgender status. But why is this cruel, while forcing other people to lie about reality not cruel? Again, it comes back to mental health. People who don't claim trans status are presumed to have more robust mental health than those who do, and, as such, it is incumbent on the former group to acquiesce to the claims of the latter, even if it costs them. Whatever the costs to the non-trans group - truth, comfort, resources, safety, it doesn't really matter, because the presumed cost to the trans group - suicide - is so high, it will always trump anyone else's claim.
I really don’t understand why people [who call themselves feminists] have an issue with them.
This is pretty straightforward. As well as the 'suicide-risk-trumps-all-other-possible-harms' claim, Gleeson is here gesturing towards a belief that castrated males couldn't possibly be a threat to women. It doesn't matter if the males in question have been literally castrated, the act of a man adorning himself with artefacts of femininity is enough to symbolically castrate him in many people's eyes. Many people seem to experience a sort of brain short-circuit when you put things associated with women (dresses, make-up, feminine pronouns, the word 'woman') together with men - they act as if the man has been stripped of his masculinity by a kind of voodoo, and thus they are unable to conceive of him as a threat. This is one reason why it is so important to use correct pronouns and clear language (i.e., not 'transwomen') when speaking about this issue.
It’s like Flavia Dzodan says: my feminism will be intersectional or it will be bulls**t.
Again, fairly straightforward. Gleeson is working from an assumption that trans-identified people share a basic condition with women, and therefore we are united in the struggle against 'gender norms' and 'patriarchy'. Superficially, it seems logical. Men are derided and sometimes even subjected to violence for violating sex stereotypes; thus, men who want to be women must be in a common struggle with women, and there is no contradiction between their wants and our needs.
This is actually the assumption that most women start from when first encountering this issue. It is only when you look more closely at what the men who 'identify as women' are actually saying and doing and advocating for, that the 'common struggle against patriarchy' notion falls apart. IMO this also demonstrates that overbroad concepts like 'patriarchy' are worse than useless for feminist analysis, because they function as a sort of dustbin into which anything anyone doesn't like about the current culture can be chucked. Women's specific issues and needs are completely obliterated by these kinds of vague, sweeping concepts.