I often dives in threesomes. I think there is real value in team diving. But, I guess I can understand a possible 'reluctance' to dive in threes, under certain very specific conditions - i.e. when an established buddy pair is getting ready to start a dive where they have a particular plan, objective, or mission, and they are assigned, or asked to accept, a third 'buddy-less' diver, with whom they are unfamiliar. I have seen this happen on boats (and had it happen to me, in fact). The third diver may have different skills (worse OR better), may have a different way of signaling underwater, may have a different style of being a buddy (swimming so close that s/he frequently bumps into another team member, or swimming off without any signal as to why, etc. That doesn't make the third diver a 'bad' diver, just different and possibly requires the established pair to change their plan
Some years ago, my son and I were diving on one of the three German U-boats sunk off the NC cost during WW2, and probably the most difficult one to dive, in terms of getting on the site under good conditions. We accepted a third diver as a buddy right before we splashed - someone who was part of the larger shop charter group, but with whom we had no familiarity, and who had no buddy.
We happened to hit the wreck that day under ideal conditions, with great visibility, no current, the sand not covering the wreck as it often does, etc. Our plan was to swim around the wreck first to get a big picture, then explore specific areas of interest. Before the three of us had even done one initial circumnavigation of the (small) wreck, our 'third wheel' signals that he is low on air and is going to ascend. We are at 115 feet, he shows me his gauge and he is down to 500 PSI on his AL80! My son and I had plenty of gas left in out HP 120s. What to do - signal to him to go up alone and wave bye-bye, or end the dive and ascend with him just in case he goes OOA on the ascent. It was the first day of a two-day charter that was going to take us back to the same wreck the next day, I felt uncomfortable -as a BUDDY - leaving him to his own devices and a solo ascent, given how he apparently blew through his gas supply, so I signaled my son that we would ascend with this third diver. My son gave me our established 'WTF' signal, but ascended with us. On the boat, I told my son (in private) that I felt a certain obligation to the third diver but that we would NOT dive in a threesome the next day. Of course, the next day, we were blown out, and didn't get back to the wreck. Eight years later I still have not been able to get back on that wreck.
The issue for me is NOT the number (2, 3, 4), it is the incorporation of an unknown into a known group. It isn't the end of the world, just a possible inconvenience.