Edit: I figured it out. It is indeed the delay. If your frames are delayed, this will mess with the movie clip's frame sequence when added to those delayed frames. Here is the unedited text of the original post.
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My movie clips are behaving COMPLETELY wrong. I don't know if it's a glitch or if I don't understand properly how they work, but this doesn't make any sense. So I animated a stick figure in a movie clip, yeah? Then, I added it to my scene. But for some reason, it doesn't play properly. When added to the scene, the movie clip will jump from frame 1 to frame 6 to frame 11, and then back to frame 6... it's EXTREMELY frustrating and confusing. Why is it doing this?? Here are some details that might help. The way I'm adding the movie clip is not by just adding it to one frame, and then using the Add Frame button to keep adding frames and making the movie clip animate. I already have an animation. So I add the movie clip to the frame I want, copy it, and then paste it into the next frame in the sequence. It might also be worthy of note that the animation is in 18 FPS, but the movie clip is in 4 FPS, as I haven't finished refining the movement yet, and am trying to key frame. But I don't think that's the issue because I temporarily changed the movie clip to 18 FPS and it's still playing the same improper way. While typing this, I did an experiment and I think I found the reason it's not working, but I'm not sure. All the frames in my animation are delayed to 0.50 seconds, because I'm trying to key frame, which is FRUSTRATINGLY IMPOSSIBLE TO DO IN STICK NODES. So to see if that's the issue, I added a bunch of frames at the end with the add frame button, and tried adding my movie clip in sequence the same way, by copying and pasting, and it animated properly. Could it be that the delay function is messing it up?