Kuzcotopia
If you can read this, you are as lucky as I am.
1. Sharia law runs counter to the modern non-Muslim ideal of the division of church and state. Sharia law is derived from both the Qur'an and the life of Muhammad and Allah (god) as the sole source of inspiration. Sharia law is often touted as god's law.
2. The vast majority of Sharia laws is already covered by existing non-Sharia based laws
3. Everyone is NOT equal in the eyes of Sharia Law. (A fundamental flaw with the system that was not apparent before modern times.)
4. Civil law or Common Law(s) are fluid and can be changed by elected officials. (Frankly, I'm not so sure Sharia Law can be dramatically changed, but even if it can be it would have to be mandated by religious authorities who instructed elected officials to make changes. Again, a smack in the face of the ideal of division of church and state.)
5. Barbaric penalties for theft of property. (Though true that not all counties sever a limb from the criminal, cutting off a limb is the prescribed method.)
6. Barbaric penalties for any form of sex outside of marriage. (Volumes could be written on this aspect alone.)
7. Systemic inequality in regards to inheritance (this alone should be enough to disqualify Sharia in civil actions even if all parties agree with the inherent inequality)
8. Systemic inequality in regards to divorce. (this alone should be enough to disqualify Sharia in civil actions even if both parties agree with the inherent inequality)
(In point 7 & 8... the idea is that the individual has rights and should never be compelled to waive those rights)
9. Death penalty for several "crimes" is no longer applicable in many counties as many have abolished the death penalty altogether.
10. Several laws apply to finance in regards to usury or the charging of high interest rates which are religiously motivated ideals that fly in the face of modern financial practices. The Sharia solution is to charge a fee for borrowing that amounts to much the same thing as interest on a given loan.
Now that's how you make an argument!