Does organic chemistry somehow defy the periodic table?
While all chemistry is unified because all chemical compounds are made from things in the periodic table, that isn't like mathematics and much of physics. In these sciences many important complexities are derivable from a simple set of axioms.

Some chemistry is simple to derive or deduce from the periodic table but not all of it. The electronic properties of iron atoms tell you a lot about many iron compounds; the location of alkali metals in the table tells us a lot about their common properties.

But carbon is odd. The properties of simple compounds follow simple periodic patterns. But there are more organic compounds (consisting of carbon skeletons, usually with C-C bonds) than all other chemical put together. The complexity and variety of carbon chemistry is almost unfathomably large. None of this is obvious or predictable from the periodic table. You can't deduce the enormous variety from the simple properties of carbon atoms or anything given in the periodic table.

That is probably the sort of distinction your lecturer was aiming at.