Plead

1. To discuss, defend, and attempt to maintain by arguments or reasons presented to a tribunal or person having uthority to determine; to argue at the bar; as, to plead a cause before a court or jury.
2. To allege or cite in a legal plea or defense, or for repelling a demand in law; to answer to an indictment; as, to plead usury; to plead statute of limitations; to plead not guilty.
3. To allege or adduce in proof, support, or vendication; to offer in excuse; as, the law of nations may be pleaded in favor of the rights of ambassadors.

In this sense, argue is more generally used by lawyers.