Reason 1: 

Using different sources of Islamic law

Each of the four major Sunni schools draws from the Quran and Sunnah as primary sources. However, when clear guidance from these sources is not available, they differ in the order and emphasis of secondary sources, such as qiyas and ijma'. This methodological variation leads to differing fiqh rulings. 

Here's a breakdown of the order of Islamic sources each madhhab considers when making rulings:

Reason 2: 

Multiple Text Meanings

Even when there was a Quranic verse or authentic hadith available, scholars may differ on the meaning:

Reason 3: 

Hadith authenticity

Even when there was a Quranic verse or authentic hadith available, scholars may differ on the meaning:

Definitions:

Qiyas - Analogical deduction

Istihsan -Juristic preference

Istislah - Welfare/public interest

Istis-hab - Linking

'Urf  - Local custom

Hadith Da'if - a weak hadith

Note:  View Glossary for further definitions.

References:

The Evolution of Fiqh. 2005. Dr. Abu Ameenah Bilal Philips.