Is a DNA molecule a single strand of polynucleotide or two of them linked together?
Hmm, I think that the teacher is actually correct and that the previous explanation, although very nicely referring to text book diagrams, is a little misleading. 

The issue here is the nature of a hydrogen bond within the DNA structure. Within a chemical context, generally a molecule is a collection of atoms primarily bonded together via covalent bonds. Hydrogen bonds, by their very nature are transient - if they weren't then the double stranded DNA wouldn't be able to opened for reading! So, a strand of DNA, from the 5' end to the 3' end is one molecule. The reverse complement strand to this is another molecule of DNA. This is important as if you were carrying out a PCR reaction (for example), you would use single, stranded DNA as primers - so this would be a molecule of DNA. Also, if we were to use hydrogen bonds as a means of defining a molecular species, then water would only be one molecule - all of those H2O molecules interact via hydrogen bonds with each other!

But what about the double helix structure? Well this is a consequence of the chemical structure of each nucleotide (and the chemical properties of those atoms), aided by the hydrogen bonding to tightly pack the atoms together - it's a form taken by the thermodynamics of the inter-molecular interactions between the two molecules of DNA. 

So, a strand of DNA is a molecule. Two strands (two molecules) of DNA give us the natural, stable, helical form.