Okay, since I've watched it The Queen's Gambit lives free rent in my mind, so here's another wannabe meta:
The thing with Beth and Borgov's rivalry is that she doesn't want to win against him to prove that A Woman Can Beat Even The Greatest Chessmaster Alive, hashtag GirlPower. There's nothing wrong with this kind of storyline, of course, but when the plot focuses about Woman X competing against All Men, it's what authors and writers seem to always go for. The issue I personally have with it is that 1. it's growing a little old, and 2. the way it's been used. Beth faces sexism, obviously, but being a woman is not the only thing she is, and not the reason why she wants to win. (She herself said something along this line to her mother, when in that first interview they couldn't stop focusing on her being a Girl and didn't even mentioned Mr. Shaibel etc.)
Borgov himself doesn't seem sexist, especially for a man who lives in the 60s, so it's not even a Revenge Against The Misogynistic Asshole kind of thing. On the contrary, Beth meets men who admire her, respect her, and support her, even if (or maybe because) she kicked all of their asses. Luchenko tells her "she's a marvel"; Shaibel says "she's astounding" (and she beat him when she was 9!); Borgov himself doesn't have any issues with being "dethroned" as the King of Chess by this young lady - quite the opposite. And he also defends her against sexist accusations in the elevator scene ("she's a survivor" etc.).
This allows Beth to have the kind of story arc/sporting rivalry usually only male characters get. Borgov is not a threat to her because he's a man and/or sexist, but because he always looks so In Control, cold and aloof and almost robotic, as precise and deadly as a machine. This frustrates, angers, and scares Beth because what she fears the most is giving up her own self-control (despite being an outwardly poised and not exactly expansive person) and surrendering to her self-destructive impulses. Her worst enemy is herself. She doesn't have just an exterior conflict, but an inner one. When she wins against Borgov, she wins against her demons. She triumphs over her worst fears. And that, let me tell you, was refreshening.
