Paul appears to be asking a rhetorical question to prove his point about how harmful and shameful (1 Cor 6:5) to the Gospel such lawsuits are. After reading this passage today, I asked myself the question: "Did I know we were going to judge angels?" The immediate response was "No". I don't recall ever hearing anyone speak on the topic. I could not recall any passage elsewhere in the Bible that references Christians judging angels. So I went looking for some commentaries on this verse.
Do you not know that we will judge angels? How much more matters of this life?
Barnes' New Testament Notes (Albert Barnes) :
Probably the reference is to fallen angels, as there is no account that holy angels will then undergo a trial... Or, perhaps, this may mean that the saints shall in the future world be raised to a rank in some respects more elevated than even the angels in heaven... In what respects they will be thus elevated, if this is the true interpretation, can be only a matter of conjecture. It may be supposed that it will be because they have been favoured by being interested in the plan of salvation—a plan that has done so much to honour God; and that to have been thus saved by the immediate and painful intervention of the Son of God, will be a higher honour than all the privileges which beings can enjoy who are innocent themselves.
Commentary Critical and Explanation of the Whole Bible (Robert Jamieson):
judge angels—namely, bad angels. We who are now "a spectacle to angels" shall then "judge angels." The saints shall join in approving the final sentence of the Judge on them (Jude 6). Believers shall, as administrators of the kingdom under Jesus, put down all rule that is hostile to God. Perhaps, too, good angels shall then receive from the Judge, with the approval of the saints, higher honors.
While this is a verse about angels being judged that I do not recall knowing, it is not clear to me how Jude 6 reflects any participation of the Saints in judging the angels.
Commentary on Corinthians - Volume 1 (John Calvin):
As, however, Paul speaks here in the future tense, as referring to the last day, and as his words convey the idea of an actual judgment, (as the common expression is,) it were preferable, in my opinion, to understand him as speaking of apostate angels.
In several places, I found reference to a verse in Matthew 29 and one in Galatians that were used to defend the stance of Christians judging angels. I am not sure that the reference of Matthew 19:28 explicitly refers to all Christians or if it was specific to the 12 disciples. While it is possible that this reference could indeed show that Christians are going to act as judges of the twelve tribes of Israel, it doesn't mention anything specific to angels. Galatians 1:8 verifies that there are angels who do present a distorted or untrue Gospel and that they should be cursed by the Saints. However, to me this verse appears to be speaking of our encounters with false doctrines and demons while on the Earth.
As such, taking into account the limited amount fo time I have devoted to studying this idea of Christians judging angels, I have reached two conclusions. The first is that although I did not remember ever hearing about this topic and did not recall the verse in 1 Corinthians, I believe that Paul wrote it as inspired by the Holy Spirit. As such, I believe that we will judge angels, even though I do not know how that judgement will take place. The second conclusion, and perhaps the most important, is that God has used this tiny verse to capture my attention today, causing me to conduct a deeper study of His Word than I would have done otherwise.
While I may not have reached any greater depth of knowledge about the topic than when I had begun, at least I now know that there have been other, much more brilliant, theological minds that have reached similar conclusions, and in reading their thoughts and study on the matter, I have learned more from God's Word. I celebrate that today I have been reminded of the truth of 2 Timothy 3:16-17:
All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: That the man of God may be perfect, thoroughly furnished unto all good works.