Hi Armin - the Trim/Boolean type confusion there is related to your revolve not being a solid. It's got a teeny-tiny hole in it right at the end of the profile curve on the underside:



If you zoom in quite a bit on that "pole" zone of the underside, you can see there is a tiny hole there, which has a small edge around it:




It looks like probably your profile curve did not have endpoints aligned vertically, one was a bit off of the revolve axis, making that result. It can be good to draw those kinds of things with a snap on to the z axis line for the endpoints to make sure they line up, or you can also turn on control points and use Transform/Align to line them up vertically.

It still is normally possible to slice a non-solid with a curve, but having a tiny edge right through the area you want to cut will tend to cause problems. Also the behavior will be more predictable with solids, since the booleans are more oriented towards dicing pieces up and determining which pieces to keep based on volumes. When you don't have volumes it can still work but the behavior will be somewhat more like trim.

The ones that worked better for you seemed to have a better alignment and so got built with a cleaner solid shape without any micro edges.

- Michael