A digression may be in order about how naturally occurring proteins are left-hand twist and a simple change in location of a single atom will make the difference between widely divergent flavors... or how mirror-image molecules will function completely differently... but that would take a lot of very dry words to convey... So I will skip the digression for now.
Terpenoids are the class of compounds (oils) that produce a lot of smells folks will recognize with their eyes closed. Menthol, cinnamon, pot, and camphor are some biggies that come to mind. Of course, eucalyptus is another. There are thousands more.
In Oz the first-aid kits include eucalyptus oil as an anti-bacterial and that is why many think you should not be eating it. And smoke is a function of incomplete combustion.
But realize the chances are good the wood you are burning is not the same species someone on the internet is ranting about... good or bad.
Look at walnut as a better example. I just saw a post here this evening talking about it as a good smoker wood! Walnut makes a compound called juglone which is a potent, widely-studied allelopath with many known effects. Do not try to grow tomatoes near walnuts, for example... There is evidence juglone is a potential cancer chemotherapy agent. It works by interrupting cell division by scavenging one or more of the four amino acids needed, stopping and killing dividing cancer cells in the process.
Eucalyptus oil is another noted allelopath...
I would not consider smoking with walnut...