I'm guessing you read one of John Norman's Gor books, probably the first in the series, Tarnsman of Gor. I only read a little of it, years ago and don't remember any details, but "kidnapped from Earth to less advanced world", "bladed combat", "slavery", "giant birds", "misogynistic point of view" all sound like Gor to me. Here's part of a review from Books Without Any Pictures:
“Tarnsman of Gor,” is basically “A Princess of Mars” with bondage and sex slaves thrown in for the aesthetic. The plot is almost exactly the same as Burroughs’. Tarl Cabot is a professor who goes hiking in the woods and is somehow teleported to Gor, the Counter Earth. Gor follows Earth’s orbit, but is on the opposite side of the sun, so we can’t see it. While on Gor, in part because of slightly altered gravity, Tarl becomes a heroic warrior who is capable of seemingly impossible feats of strength and valor. He rides on a giant bird called a tarn. Tarns are treated a lot like the sand worms in Dune; they’re integral to society, but they’re dangerous and can kill people. While on a quest, Tarl falls in love with Talena, a warlord’s daughter, and when she falls into enemy hands he must rescue the damsel in distress.
Based on the outraged reviews, I had expected the S&M parts to be a lot worse and/or more sexist than they were. Yes, the female characters tended to either be sex slaves or to wear veils and and be socially segregated from the men, and I can see how that might bother some people. But, to be fair, the heroine didn’t end up chained up until she tried to kill Tarl several times, and he did seem to be very respectful of her under the circumstances. Then again, I also probably wouldn’t fall in love with someone who tried to kill me, so there’s that.