Fly/go off at a tangent
Definition 1 of 2
Pro Tip 1/3Sudden Shift
The phrase is used when someone abruptly changes the topic or plan, without warning. 
Mid-conversation, she flew off at a tangent, discussing her vacation plans.
Pro Tip 2/3Unexpected Topics
When used, it often implies that the new subject is surprisingly different or unrelated. 
While discussing taxes, he suddenly went off at a tangent about space travel.
Pro Tip 3/3Informal Expression
The phrase is casual and best used in informal conversation or creative writing. 
In our book club, discussions often fly off at a tangent and become very lively.