A republic is simply a state without a king or other hereditary monarch. Often the leader is chosen democratically, but not always.

For example, China is a republic but not a democracy. The US is a democratic republic, which makes the claim "this is a republic not a democracy" even sillier.

Never believe that anti-Semites are completely unaware of the absurdity of their replies. They know that their remarks are frivolous, open to challenge. But they are amusing themselves, for it is their adversary who is obliged to use words responsibly, since he believes in words. The anti-Semites have the right to play. They even like to play with discourse for, by giving ridiculous reasons, they discredit the seriousness of their interlocutors. They delight in acting in bad faith, since they seek not to persuade by sound argument but to intimidate and disconcert. If you press them too closely, they will abruptly fall silent, loftily indicating by some phrase that the time for argument is past.

--Jean-Paul Sartre