Sqad is absolutely correct. Whilst monozygotic (identical) twins do have the same genes, their mitochondria are not identical as they contain different mitochondrial DNA. In practical terms, this means that each twin can react differently to everything from cigarette smoke in the environment to foodstuffs. In addition, they can also respond differently to infections and medications.
Research by Bruder and Dumanski at the University of Alabama has also shown that something called copy number variation (CNV) is also responsible for response differences in monozygotic twins. CNV refers to differences in the number of copies of an individual DNA segment between two or more genomes ( A genome is the full complement of genes carried by a single set of chromosomes). CNV can occur when pieces of DNA are missing from the chromosomes of the parent, causing the offspring to have only one copy of that piece of DNA. Furthermore, mutations can produce many copies of a particular “bad” bit of DNA. What this means is that twins are not 100% identical as their DNA can be minutely different due to CNV. Prior to this research it was often thought that the environment was the reason why one monozygotic twin would develop a disease such as Crohn’s disease or have a differing susceptibility to AIDS over another monozygotic twin. Incidentally, there is even a specialist name for identical twins that display such variations: they are called discordant monozygotic twins
As far as your teacher’s concerned mollykins, this sort of stuff is not particularly advanced and is taught during routine genetic tutorials to students taking basic BSc biology degrees at universities throughout the world. The only thing I can add is that I’m absolutely certain he’s not a life sciences graduate of any of the colleges at my university!
Never mind - just ask him next time you see him to explain discordant monozygotic twins to you!