exactly! they're jealous af that arya is a more important character and has different plots, not only both magic and political importance w leadership foreshadowing, but also a romantic one. while they're stealing aspects of her arcs for themselves, they need to "prove" why she can't have those. that's where forcing arya into "tomboy" tiny box comes from. "arya is a tomboy", "she doesn't have to be feminine", "she doesn't have to be pretty", "why are you sexualizing her", "calling her pretty gives p*do vibes", etc, etc.
one of their bullshit made up narratives was that arya's plot from og outline was cut in two and the romantic aspect of it grrm gave to sansa, thus jonsa instead of jonrya. they tried to make the same about lyanna: actually both sisters are paralleled w her, and arya has horse riding/sword playing i guess, while sansa got the songs and romantic part. (i lost like. years of life just typing this nonsense 💀)
but oops, arya stans debunked this shit absolutely and since then they started to use misogynistic arguments against lyanna as well. "if we can't have this, no one can" it seems 🤷🏽♀️ "parallels w lyanna aren't a good thing actually", "northerners would hate lyanna for starting a war", "manwannabe", 1536372 wild bullshit claims from the cultists, "rhaegar and lyanna ain't a love story" - and this one has different roots tbh. it's both anti targ sentiments all over again AND an implication that girls like arya and lyanna can't have princes falling in love w them, especially not over "lady-like embodiments of femininity". they can't accept the fact that grrm gives romantic plotlines to girls who don't conform into society's restrictions for women intentionally. because deep down they ARE misogynistic and want their obedient good girly girls have all the goodies while "bad disobedient" ones have nothing and are even punished for not fitting in.
parallels w lyanna just show once again what a beautifully written, complex and multidimensional female character arya in fact is. it's smth they don't want ppl to acknowledge bc they both feel threatened on behalf of their own self insert fave and bc, like i've just said, they're misogynists who can't accept the fact that women not bowing down to patriarchal society's demands are worthy of the same things that the rest of women are, that they are allowed to have this and that they DO have all of this.