You've seen some of these movies before. You're all familiar with this plot beat. The woman, almost always a love interest, has been captured by the villain, and the hero has to brawl or bargain to save her. There's nothing inherently sexist about the situation, just as the use of such a plot device doesn't automatically make a movie sexist. But that's beside the point. This supercut puts a lot of unpleasant Hollywood trends in stark relief.
For starters, notice how in most of these clips the woman doesn't even speak. She's a prop. The only important dynamic in the scene is that between the (generally) male hero and the (generally) male villain. Their relationship is the important one, the real one, the dramatically resonant one. The men have all the dialogue, all the power, all the agency, all the charisma, all the audience's rooting interests--everything. Meanwhile, the women just have weakness and manufactured tears. They are little more than poker chips in these scenes, an observation driven home when the heroes start offering money to trade for her: "I'll give up the gold," "I gave you the money," "I'll open the safe." Then, as if it wasn't apparent enough, we have the litany of scenes that make the utter unimportance of the woman explicit: "This is between you and me," "She's not important," "She doesn't belong here."
If she's really so unimportant to the central conflict, why is she even in the movie? The answer is even sorrier than the question: She exists in these films as nothing more than a pawn, a plot device, and an eventual reward for the man to take home and mount on his mantle. Figuratively speaking.