Is this analogy explaining the difference between enantiomers and diastereomers correct?
Enantiomers are non-superposable mirror images (all the signs of one spatial coordinate are reversed).  Diastereomers are  formed by inverting some but not all stereocenters.

http://osf1.gmu.edu/~bbishop1/CHEM%20814-579%20Stereochemistry%20Lecture%20slides.pdf  
 pp. 11-13.  Excellent overall.

Have some fun with your prof!  An acyclic, aliphatic, unstrained, tetrahedral carbon atom is $\ce{sp^3}$-hybridized.  It is an uncharged, valence-saturated singlet.  It bears four freely rotating, rigorously identical substituents, e.g., $\ce{CR4}$, with identical bond lengths to that central carbon.  Said carbon is a chiral center.  It has no ${S_n}$ improper axes of symmetry.

1) Show how this can be true. 
2) Use any system of nomenclature to name left-handed and right-handed stereoisomers.

Acyclic, unstrained, etc., trigonal planar $\ce{sp^2}$-hybridized carbons ${R2&gt;C=C&lt;R2}$ are each identical stereocenters.  Each carbon and the olefin overall have no ${S_n}$ improper axes of symmetry.  The olefin is resolved chiral.  (1) and (2) as above.