so. bisexual has, historically, always meant attraction to one's own gender and to others (so, for example, a bisexual man is attracted to men - his own gender - and to women). as the ideas of non-binary and trans people became more mainstream, there was always an understanding that bi people were including those people in their definition - so, for example, the same hypothetical bi man is attracted to men (and trans women) and women (and trans women). that was broadly understood by people in the community.
then as these ideas went even more mainstream and being not-straight began to gain some social capital, younger people with a desperate need to be special latched onto the idea that "bi" means "two" and therefore bi people are attracted exclusively to cis men and women. (never mind that, like, this shit is personal and case-by-case anyways - being attracted to women generally doesn't mean you're attracted to every single woman, etc., but nuance is not these people's strong suit.
so they developed the idea of "pansexual," which is supposedly an attraction to "hearts not parts," i.e., an attraction regardless of gender. they also decided bisexuality was inherently transphobic. this is bullshit because: (1) gender is part of attraction, it just is (2) what they're describing - an attraction to men and women both - is called bisexuality. bisexuality never excluded trans people by default. (again, attraction is more complicated - some bi people will like some trans people, vice versa, that's how the world works, but again, these people just want to be holier than thou.) finally, there's something really weird about bragging that your sexual attraction is not based at least in part on bodies and sexual compatibility because that's just not true.
also, and I really am almost done, separating out trans people as a group to be attracted to, as opposed to just automatically included in any given gender, is seen as transphobic. (i.e., if you say "bi people are attracted to men and women, pan people are attracted to men, women, trans men, and trans women" you're essentially arguing that trans men/women are some separate other gender.)
so the Tumblr post is saying, in Tumblr-speak, that going "uwu im pan, hearts not parts uwu!" is just shorthand for "I want to be more special than bi people, and I don't consider trans men to be men or trans women to be women, but rather some special extra gender." so, if you consider that statement to be trans or biphobic, and if you consider those things to be a problem, the post makes sense.
tldr: this shit is so fucking dumb. pansexual is just a dumb extra word for bi, which already exists.