【 the meaning of 'sell a contradiction' 】 について
ｶﾅﾀﾞ ﾌﾞﾘﾃｨｯｼｭ・ｺﾛﾝﾋﾞｱ州のCanadian English話者のコメント（Word Reference.com Language Forums）

To sell a contradiction would probably mean to convince someone of the rightness
of something even though it is a contradiction with something else.

You'll note that I said "probably", Stenka(質問者の名前). Now, I'll give you my spiel about pop music...
don't use it to learn English.;)

The lyrics to music (especially pop music) are written so that they are accomodated in the tempo,
meter and mood of the song. In this case, the writer had to find a word that rhymes with "conviction"
- she/he chose "contradiction" - it's that simple.

Pop music is rife with bad grammar and sometimes incomprehensible word groupings
and, in many cases, your guess would be as good anybody else's.