From wikipedia Cut to the chase
Cut to the chase is a saying that means to get to the point without
wasting time.
The phrase originated from early silent films. It was a favorite of,
and thought to have been coined by, Hal Roach Sr (January 14, 1892 –
November 2, 1992). Films, particularly comedies, often climaxed in
chase scenes to add to film time. Some inexperienced screenwriter or
director, unsure how to get to the climax or the lack of script to
meet time requirements, would just make an abrupt transition, known as
a cut. The phrase is unusual in that its common meaning of "Get to the
point" is opposite to its logical meaning of "I am completely out of
ideas and have ten minutes to fill up. I'll just give them ten minutes
of chase."
It appears that "cut to the chase" does not mean to transition from one topic to another in an abrupt manner, but rather to focus on what is important and of main interest; i.e., in the case of silent movies between 1912 and the mid 1920s; the then famous, Keystone Cops, car chase scenes.
Idioms that share similar meanings to cut the chase are:
Positive
- To get to the point
- To get to the core
- To get to the nitty-gritty
Vulgar but effective
Ambivalent
- to skip over something.
To omit something; to avoid reading or looking at something
EDIT:
One possible one-word expression which carries negative connotations and can mean to miss the main point of a topic or an argument is
Overshoot; to shoot or go over, beyond, or above; miss.
Otherwise, if I wanted to say that someone doesn't move smoothly from one thing to the next; I would say he's jumping from one subject to another.
Jump To move discontinuously or change after a short period and "A sudden or major transition, as from one career or subject to another."