It’s extremely difficult to square this ruling with the text of Section 3 [of the Fourteenth Amendment]. The language is clearly mandatory. The first words are “No person shall be” a member of Congress or a state or federal officer if that person has engaged in insurrection or rebellion or provided aid or comfort to the enemies of the Constitution. The Section then says, “But Congress may by a vote of two-thirds of each house, remove such disability.”
In other words, the Constitution imposes the disability, and only a supermajority of Congress can remove it. But under the Supreme Court’s reasoning, the meaning is inverted: The Constitution merely allows Congress to impose the disability, and if Congress chooses not to enact legislation enforcing the section, then the disability does not exist. The Supreme Court has effectively replaced a very high bar for allowing insurrectionists into federal office — a supermajority vote by Congress — with the lowest bar imaginable: congressional inaction.
This is a fairly easy read for the legal layperson, and the best general overview I've seen yet that sets forth the various legal and constitutional factors involved in today's decision, including the concurring dissent by Justices Kagan, Sotomayor, and Jackson.
Honestly, that part of the amendment is just horribly written. It reads like a rush job, which is probably was given it was written to remove/keep out former Confederates. There's no mechanism in there to determine guilt or any definition of what constitutes insurrection or rebellion. Seceding, forming a new government, and declaring war on the US is obvious, but it doesn't say what the minimum threshold actually is. The entire thing is just two sentences. This very comment has a similar word count.