"If you dislike the amount of coverage Swift is getting, you're automatically misogynist" is a pretty weak rebuttal.
First off, Swift is like the most popular person in the world. Her presence at NFL games has garnered more attention than any other celebrity I can think of. What's the stats on Eminem and Matthew Mcconaughey compared to Swift? And did Cowherd really just say Nicholson was "celebrated" as a Laker's fan in the 80s and 90s? Everyone who wasn't a Lakers fan got absolutely sick and tired of seeing him over and over every game, and were vocal about it. However, unlike Swift, I don't recall sports shows, articles, etc spending much if any time at all talking about Nicholson.
If you Google NFL news, you're going to find articles about Taylor Swift. If you watch ESPN, you're going to hear about Taylor Swift. I don't recall this being a thing with Eminem, Matthew McConaughey, or even Jack Nicholson.
When Russ and Ciara got together, I don't recall her being shown during the broadcast all that much. I don't recall seeing articles every day about them, either. Even so, the amount of discussion and attention it garnered was somewhat irritating. Same with Tony Romo and Jessica Simpson to an even greater degree.
The common denominator here is not women. It's the continued obsession with who star athletes are dating. It gets more attention than their children, their parents, the charities they donate toward, etc. Talking about who's dating who is like the lowest form of gossip in existence. Now we have star NFL tight end on multiple super bowl winning team dating the most famous person in the world. So yeah, people are going to bitch about it to a higher degree than the examples I listed above.
If Travis Kelce was dating Justin Bieber instead, people would still complain. Although, I'm sure the narrative would change from misogynist to homophobic. As long as they get to claim that people are bigots. That's what they love to do.
"Insecure men"... Give me a break. Even if insecurity is at play, is that supposed to be an insult? Insecurity involves mental health. Therefore they are insulting people with mental health disorders. Why is it generally accepted to insult men for being insecure? Seems sexist. See, I can play this game too.