My professor said that this compound is an enantiomer but I think it has a plane of symmetry and has no chiral carbons. Am I missing something ?
The comments are right. The molecule shown is not chiral and will not show enantiomerism.
But still, remember that an alkane ring, unlike an aromatic ring, is generally not planar and take that into account when evaluating molecules. Thus chloromethylbenzenes with a planar ring are never chiral, but chloromethylcyclohexanes will be chiral if the chlorine and methyl group are not on opposite ring carbons.
Since a cyclohexane has a bond angle which is quite close to tetrahedral bond angle, the molecule is not planar. Similarily, p-chlorotoluene would also not be planar.
If you observe the conformers of cyclohexane, you would realize that the chair and boat conformers are non chiral due to chair conformer having an alternating axis of symmetry and the boat conformer having a center of symmetry. But the twist conformer is chiral.
Similarily, if we substituted any two of the hydrogens with a methyl and chlorine group, we would get many more conformers which would be chiral since the new molecules would not have the plane of symmetry or the alternating axis of symmetry which the orginal molecule had. Therefore, I would say that the molecule is chiral though you should confirm it with your professor since drawing the conformers of a molecule is difficult and there can be exceptions.