Here's the way I understand it...
You can take something like sandalwood and put it in a gas chromatograph. This will give you a list of the main esters present. It might include:
Monocyclic sesquiterpene alcohols
In a lab, they make these chemicals using a number of different methods, including transesterification, condensation with acidic protons, rearrangement of haloketones in presence of base, nucleophilic displacement of alkyl halides with carboxylic acid salts, nucleophilic displacement of acyl halides with alcohols, oxidation of ketones with peroxides, and reaction of nitriles with an alcohol. Some of these processes even occur in plants... think of them like natural little mini-laboratories.
So, yes, you can chemically reproduce the results of the gas chromatograph, and get something that smells very close.
But why not exact?
Because there are TRACE esters present. Sometimes thousands of them. Individually they don't contribute anything noticeable, but combined together, they produce the subtle nuances that can only come from dozens to hundreds of trace esters present in the natural substance.
It WOULD be possible to reproduce all the trace esters detected in a gas chromatograph, but it would be so costly, it wouldn't make any sense to do over using traditional extraction methods with the natural substance.
The quality of synthetics can be measured on how many trace esters and other aromachemicals they include. Higher quality synthetics utilize more trace esters to produce a more natural smelling synthetic while still keeping the price cheaper than the real thing.
Synthetics are not bad. They are used in virtually every perfume available today. For example, Chanel No. 5 includes civet musk as an ingredient. This is an animal product that comes from scraping the musk glands from a live civet, something that harms the animal. In 1998, Chanel stopped using real civet musk due to ethical concerns and switched to a synthetic. Most people didn't even notice.
So synthetics are not bad. They are used all the time and are blended with natural ingredients to create scents that were never possible before.
Take a look at the synthetic base page on Perfumer's Apprentice. I would avoid using very cheap "fragrance oils" from places like saveonscnets to make high quality perfume and cologne.