I don't think you can drag a copy to a new layer as you are creating it (it's definitley counter intuitive). When you make the selection of the object you want to copy you are activating the layer it's on.
I think I would drag the copy and leave it selected, then move it by dragging the little square on the right of the object or layer name in the layers panel (depending on if the layer is expaneded) onto the correct layer.
When working in the document page you will not be able to create the object and move it on a different layer at the same time however if you are working in the layers panel then you could use "ALT" key to create the copy of the object and move it on a different layer.
NEITHER OF YOU READ MY MESSAGE CORRECTLY.
InDesign IS changing layers as I drag to copy! I am asking HOW TO PREVENT LAYER SWITCH from happening. I want each copy to stay on the same layer as the original, not change layers as I drag.
It doesn't happen every time, but it does at least half the time. So then I have to take extra time to cut and paste it to the layer it should have been on in the first place.
As Peter and Manish implied, this is NOT normal behavior for InDesign.
So I'd look to troubleshooting techniques. Start by restoring your preferences:
If it only happens with one document, it may be corrupted, and you may want to save as IDML and reopen in InDesign.
Thanks, but I tried both of the above and neither helped. It still switches occassionally, not every time.
I also tried a brand new, blank document. I created two layers, one for text (top) and one for artwork (bottom). Whenever I opt-dragged a text box over artwork in another layer, it went to the artwork layer instead of staying in the text layer. Same thing if I copied artwork and dragged it "under" the text box, the new artwork went to the text layer instead of staying in the artwork layer.
If I did not overlap items when I copied, the new copy stayed in its proper/original layer.