I'm going to take this in good faith and assume you truly are open to being educated here, but I will caution you that this is right on the line of something I would remove (transphobes often use questioning similar to this to troll and harass the trans community).

Grover's insistence on referring to Tickle as a man reflects an (intentionally) limited and outdated understanding of gender, as well as a clearly spiteful attempt to hurt and disrespect Tickle.

Lets first address the biological aspect. Firstly, "biological sex" (itself a fairly outdated term) is more complicated than simple chromosomes. Yes, most people with XY chromosomes are assigned-male-at-birth and have the corollary primary and secondary sex characteristics to match, but that doesn't make it universal. For instance, individuals with Swyer Syndrome are born with XY chromosomes but develop female characteristics, including uteri, and can even give birth with IVF.

Furthermore, the medical community has long generally drawn a distinction between sex (your biological characteristics) and gender (a complex psychological and social identity). This awareness has been present in Western medical thought since the 1950s, following research by J Money and others. Gender identity represents more than biological characteristics and is about how people perceive themselves and live their lives. Grover's ideas also loosely play into the notion of biological essentialism, an outdated idea that a self proclaimed feminist such as herself should be rejecting (Simone de Beauvoir was writing about this in 1949!).

It can be pretty difficult for a cis (not trans) person to understand what it feels like to have a misaligned sex and gender, since yours are largely indistinguishable, so let me give you my personal experience (with the disclaimer that it is not universal, everyone is different). For me, it was a largely unplaced discomfort with my body and hatred of my "masculine" features. I was maxing out about every depression metric, even as a toddler. When I eventually connected the dots and began medically transitioning (taking testosterone blockers and estrogen) this discomfort eased significantly. My body and (occasionally) how society understood me finally matched how I understood myself. It felt like I had been suffocated my entire life and was finally able to breath.

From a practical standpoint, you are almost always using pronouns and titles based on your perception of a person's gender identity and presentation - it is not reasonable to perform a DNA test on everyone you meet. On a deeper level though, when interacting with others, using pronouns and titles that align with their gender identity is not just a matter of politeness but a recognition of their humanity and autonomy. Misgendering someone invalidates a person's identity and can contribute to their distress and alienation. To do this intentionally is fundamentally disrespectful, rejects decades of medical progress, and ignores the personal experiences of the target.