1.
one's pet theory, personal opinion, cherished view
A strongly held personal opinion or viewpoint that someone consistently maintains and expresses. Often implies the person has held this view for a long time and brings it up regularly.
It's my grandfather's pet theory that waking up early is good for your health.
Usage
持論 always refers to someone's own opinion, typically one they have held for a long time and express repeatedly. It can be neutral or slightly dismissive depending on context — when used about others, it sometimes implies the opinion is idiosyncratic or unproven.