I was working on a model when I encountered this problem while trying to bevel an edge. I'm not sure what's causing this even after I've tried merging duplicate vertices and applying the scale. If anyone knows what might be causing this issue, I'd love to know why this is happening.
Edit: As per Allen's suggestion, I've added a simplified version of the model with the problem edges marked with red seams. They don't exactly replicate the GIF I've posted, but I think it's a similar problem nonetheless.