There are two type of differences among groups:
- Difference in beliefs views
- Difference in Fiqh views
The first one is what makes sects (Sunni, Shia, etc..), and it's actually a disaster. This difference shouldn't have existed at all. The whole Muslim Ummah should be united, we should follow what the prophet said "Follow my Sunnah, and the Sunnah of the Rashidi Khalifes succeeding me. Hold it with your teeth".
The second difference, which is difference in Fiqh, is what makes Mathahib. This difference has reasons, and is completely acceptatble (these differences doesn't have to be resolved), in fact Allah has a great wisdom about it, of which is mercy upon muslims so there's no very strict rules that may be hard to do, instead there is an ability to extract rules out of sources and, since sources (much of the times) can have more than one meaning or can be understood in more than one way, then it's very normal to have difference Fiqh views, this is not a bad thing (if it was, then Allah with his mercy wouldn't allow more than one understanding to his Ayat), in fact "flexibility" is one major "feature" of Islam.
The following hadith is an evidence that Islam encourages deriving rules (if the one who derives has the knowlegde):
'Amr bin 'Al-'As (May Allah be pleased with him) said:
I heard the Messenger of Allah (PBUH) saying, "When a judge utilizes his
skill of judgement and comes to a right decision, he will have a
double reward, but when he uses his judgement and commits a mistake,
he will have a single reward."
[Al-Bukhari and Muslim]
وعن عمرو بن العاص رضي الله عنه سمع رسول الله صلى الله عليه وسلم
يقول: "إذا حكم الحاكم، فاجتهد، ثم أصاب، فله أجران، وإن حكم
واجتهد، فأخطأ، فله أجر" ((متفق عليه)).
Although agreement (Ijmaa) is preferred, there is no problem at all having different opinions among Mathahib, because all mathahib don't derive rules from nothing, they absolutely but evidences.
An important fact to know is that the four Imams (Imam Hanafi, Imam Malik, Imam Shafei, and Imam Ibn Hanbal, may Allah be merciful to all of their majesties) where students of each other: Malik was a student of Hanafi, Shafei was a student of Malik, and Ibn Hanbal was a student of Shafei. They all greatly (and, in truth, amazingly) trust, love, and respect each other, the difference in Fiqh views is because of reasons, reasonable reasons. If the four Imams where very respectful to each other, they why followers should fight? this is a nonsence.
(Note: to understand really why having Mathahib is acceptable and a good thing in Islam, you should ask about the reasons for having different Fiqh views).
Sources that helped in making the answer:
A final thing I would like to say is that I agree to ashes999 answer.