Straw man
Etymology
A "man of straw" was a seventeenth-century term for a sham or worthless person — a stuffed dummy standing in for the real thing. Whether the argumentative sense comes from that idiom or from straw-filled figures used in combat drill is disputed. Either way the image is the same: knock down a fake because the real opponent is harder to beat.
noun phrase · /STRAW-man/
Refuting a distorted, weakened version of someone’s position instead of what they actually argued.
What it names
Catching it stops you from conceding a "defeat" of a claim nobody was making.
Example
He said we wanted open borders with zero screening, then attacked that — but our proposal was just faster visa processing, a pure straw man.
Related idea
Unlike a red herring, which changes the subject entirely, a straw man stays on topic but misrepresents the opposing view.