Sophism

Sophism can mean two very different things. In Ancient Greece, sophism was practiced by "sophists", who were a group of teachers of philosophy and rhetoric. In the modern definition, a sophism is a confusing or slightly incorrect argument used for deceiving someone.
Etymology.
The word "sophism" originated from the Greek word σόφισμα, "sophisma" (from σοφίζω, "sophizo" meaning "I am wise"). 
The similar Greek word σοφιστής, "sophistēs" means "wise-ist, one who does wisdom, one who makes a business out of wisdom" while σοφός, "sophós" means a "wise man".
History.
The ancient Greek philosopher Protagoras 
(ca. 490–420 BC) is often said to be the first of the sophists. Others include: Gorgias, Prodicus, Hippias, Thrasymachus, Lycophron, Callicles, Antiphon, and Cratylus.
Plato opposed those sophists because they only abused wisdom for their own interest and refused the truth and justice.
Modern usage.
In modern usage, "sophism", "sophist", and "sophistry" are derogatory terms, due the influence of many philosophers in the past. Sophism and platonism were rival schools, as enemies of each other.
A "sophism" is a statement to deceive someone in a debate or conversation. It might be made to seem to make sense when really being wrong, or it might use difficult words and complicated sentences to intimidate the audience into agreeing. An argument "ad hominem" is an example of sophistry.
A "sophist" is a person who uses sophisms. "Sophistry" means using sophisms for subtly deceptive reasoning or argumentation.