Argue irrationally, having a screwy point (5)

I believe the answer is:

auger

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'a screwy point' is the definition.
'auger' can be an answer for 'point' (thesaurus). I am unsure of the 'a screwy' bit.

'argue irrationally' is the wordplay.
'irrationally' indicates an anagram.
'argue' anagrammed gives 'AUGER'.

'having' acts as a link.

Can you help me to learn more?

(Other definitions for auger that I've seen before include "Tool for boring holes in wood" , "A tool for boring hole in wood" , "Boring-tool" , "I bore" , "Boring instrument" .)

I've seen this clue in the Evening Standard.

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