But you also have a different diagram in which B has been removed; a different object.
Purge from your mind a whole aspect of who you are, and some other two parts become disconnected: uncontroversial to me.
The example also works the other way. In a hypothetical example of two non overlapping circles teaching and PHD don't suddenly overlap just because you draw a new circle encompassing some 3rd idea.
Saying A relates to B and B relates to C says nothing about A relating to C.
Picture a ven diagram where A overlaps with B, B overlaps with C, but AC does not overlap with A. Remove B and you have two circles that don't overlap at all.