Does your uni only have unisex toilets?
Building regs says that there have to be separate women's and men's toilets, unless there is no space - a large public building like a university is unlikely not to have enough space, so it's likely they are obliged to have sex-segregated toilets.
They can add unisex ones if they wish, but a 'universal' toilet is something specific according to building regs, it's not a single-sex toilet with a new unisex badge slapped on, so they can't just re-label the women's or the men's as unisex.
So the situation you rightly criticise, where visiting children have to share toilets with adults of the opposite sex because there is no alternative, should not arise if building regs are being adhered to.
There are so many valid arguments against unisex-only provision, from safety to dignity to religion/culture, but I like the directness and clarity of quoting the law and building regs.
An optional extra argument is that there is already a tried-and-tested, long established arrangement of men's, women's and disabled toilets, which worked well until a very small number of men started demanding access to the women's toilets.
There has to be a better rationale for changing this established toilet provision - involving a lot of disruption and expense - than a tiny number of men feeling uncomfortable or claiming, without any evidence, to be in danger in the men's toilets...