Why does snapping to an object to draw a line join that line and that object?

I see only normal behavior in your video and I don’t think I understand you question from the title alone.

You are using the pencil to trace over an existing edge which has been hidden. When you complete the pencil operation you have a visible edge between those two nodes, this is the expected action of the pencil tool, to create an edge (line). The circle is still a circle, you have made one hidden edge visible. If you want to “cut” the circle then draw two perpendicular lines connecting to nodes you want to isolate to “cut” the circle. If you wanted that edge not to merge with the existing geometry you should make the geometry a component or group to isolate it so that it will not interact with other geometry before using the pencil tool.

Always good to explore the basics when beginning.

The hidden circle IS a component. You can see it in the clip when I select and drag. But when I try to offset just the line everything offsets. I have deep experience in MicroStation and AutoCAD and this component thing is UI weirdness.

The geometry on the screen is clearly not a component as I can see individual faces and edges in the video. If it were a component it would all have a blue rectangular bounding box. It looks like perhaps just the hidden line circle was saved as component but that one on the screen is not, perhaps because you didi not have the “replace selection with component” checked when you saved it. The SketchUp UI is and general logic is well thought out and executed. Like any complex program it has it’s own language and set of core ideas to comprehend, the Campus link I posted is a great place to get up to speed quickly. Proficiency in other CAD platforms will not necessarily help you in using SketchUp.

It might be easier if you described what you are trying to accomplish and include a copy of the .skp file you are working with in your reply.

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When you have a non 3D object, like a circle a square or a line and you want to make them components you have either to group them first or on the component window select replace component with selection otherwise they will remain as loose geometry. If you share your file we can check what’s going on and give you a solution.

why would you make a component out of an hidden object ? there’s no logic about that. at a pinch you could make a component THEN hide it, but there’s no point turning a circle that is part of a wall into a component either.

Group or turn the whole thing into a component then draw your lines over it before you offset anything.

Drawing over an hidden edge that is part of an entity such as a circle will just make sketchup think you are wanting to reveal part of it, and offsetting it will act on the entire entity. It would act the same way with an arc.

your second video does not prove anything. Having a component that is a circle doesn’t necessarily means the one your are drawing over is this very same component, as far as I can see it is just loose geometry.