They are Pashtuns, the dominant tribe in Afghanistan and feel that governing Afghanistan is their right. They are also insurgents using guerilla warfare techniques because they are outgunned from a technological standpoint and have no air power.
Most, including Muslims, have little sympathy for the Taliban's harsh religious beliefs. For the U.S. it is a question of knowing the enemy. Ignorance of the enemy's intentions, belief systems, and will is a recipe for disaster. Evidence Exhibit A: Eight years and five months of war since the U.S.-led NATO invasion of Afghanistan. Evidence Exhibit B: The Red Army invasion of Afghanistan, resulting in ultimate defeat after eight years of war. Evidence Exhibit C: Afghanistan is the graveyard of empires (see opening paragraph of this article).
Karzai wants Omar to attend that jirga, but the U.S. has not given the "green light" to Omar's right of passage to the event. What actually precipitated Baradar's arrest remains a mystery. However, it raises questions about whether the U.S. is willing to back peace discussions with top leaders of the Taliban. In the past, the U.S. position has been to negotiate with mid-level commanders of the Taliban, not the likes of Omar. Obama's "suggestions" do not change that dynamic.
Karzai is reported to have said, "Our allies are not always talking the same language," no doubt adding to his frustration. I have the deepest lack of respect for the so-called mayor of Kabul -- he is corrupt, his administration is corrupt, his family is corrupt, and there are deep reservations as to whether or not he is a nationalist leader -- but, perhaps in this case, he has a point.