You are quoting the respective scripture at each other (both the same of course) This is equally applicable to any scripture based religion.

So you can throw quotes at Christians from Leviticus and be retaliated with some Deuteronimus.

Or in your case a Muslim could say, yes, well those quotes are in the Qur'an, but here it says...

The problem with quoting out of context is, that you can always bend any quote in the direction you like and if you don;t like it - ignore it.

It is not helpful and does not lead to a solution of the underlying problem.

So applied to our situation. A Muslim that reads the quotes will not (necessarily) loose faith, because his convictions are stronger (as are yours) to resist and ignore the inconsistencies.

If that would work... One of the oldest stories in the quote war is Gen1 against Gen2 - two completely different stories - even in English, and if you look at the original the differences and contradictions get even greater. how can anybody believe that Gen1 is an acurate description of historic occurrence, when Gen2 tells a complete different creation story.

That argument has however rarely stopped a Gen1er in his/her stride. They rather try to ignore or somehow forcefully incorporate it in their convictions.
That's why quote war's are usually not convincing. Especially from a Non-literal point of view (be it enlightened believers, or atheists, which will use similar arguments to the former)

This does not mean that small battles cannot be won, but it will not solve underlying problem.
Someone that believes in the literacy of hisher holy scripture is not going to fall out of his/her faith simply because of inconsistencies in the text. (Our mind is to small to understand this, have faith and it will become clear... or some such quote)
I don;t have a solution to the problem of how getting people away from their rabbit-eye-stare faith. Otherwise I would be a minister now....