The words 'averse' and 'adverse' differ by only one letter. But they don't mean exactly the same thing, and only 'averse' can be used in the construction 'I'm not averse to . . .'. If you write 'I'm not adverse to . . .', you are incorrect.
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The Macquarie Dictionary defines 'averse' as meaning "having strong feelings of antipathy or repugnance; opposed'. For our purposes, "opposed" is the relevant sense. 'I'm not averse to' means the same as 'I'm not opposed to'.
That double negative construction isn't the ultimate in clarity, but it is widely employed. Unfortunately, the incorrect 'I'm not adverse to' is also often used. While 'adverse' also means 'opposing' (in a broad sense), it occurs in structures such as 'adverse reaction'.
It's an easy mistake to make, especially if you've misheard the expression. You're admittedly unlikely to be misunderstood if you use the wrong version, but you will still be wrong. And no-one wants that, do they?
Lifehacker's Mind Your Language column offers bossy advice on improving your writing.