The TL;DR Synopsis (if you just want my point)
The simple truth is that a lot of the backlash of the death of solo queue is from people who treat League of Legends as a single-player experience and forget it is a team-based game focused on taking objectives, and working together to defeat the enemy TEAM. Yes, the fact that people who play alone no longer have the option to expect to face other lone wolves is a topic for contention, and one I would happily have a discussion upon. But a lot of people angry with the death of solo queue are only angry because the dynamic queue shift hurts their ranked progression because of HOW they play in Ranked, and wouldn't care - beyond excusatory griping - if it had no affect on their performance.
Solo queue is an appropriate name for the previous method of queueing, because it promoted League of Legends for those who bear a highly selfish mentality, and their mentality did nothing to punish them when they were progressing in ranked. While there is an obvious need to have some degree of self-interest in your playing of League, the community at large has been shaped by a 'me' vs a 'we' mentality when it comes to playing what is a team game. Even in solo queue, the duo queue was hated, but not simply because it presented an advanced avenue for trolls to take games hostage, but because people had the idea that 'your rank should only indicate your personal skill,' with the consensus of personal skill being the sum of game knowledge, mechanical ability, reflexes, and strategy.
But those aren't the only avenues of improving oneself, yet anything more is dismissed due to a lack of 'personal' application, that is: if it involves anyone other than yourself (and the enemy), it isn't your sole contribution and ergo does not count.
(For those who don't mind reading a novel)
Thee problem with the solo queue vs dynamic queue debate is that some people only want to play by themselves (of which there is nothing wrong inherently, and the option for such should always be fully supported), but among those people are a number of individuals who would in turn force others to only play by themselves in ranked as the only option they will tolerate.
It's always possible that some people don't want to make a team because they don't want to socialize with others, which is completely understandable, and you shouldn't have to make a team just to be able to keep up with others.
Not all of the backlash is because of the removal of choice (which is where the primary focus of complaints should be), part of it is simply because the new teamwork orientation in ranked disfavors the solo queue-style neglect of teammates. Some people believe rank is entirely indicative to be a measurement of personal skill, and that your cohesive ability in a team is not something that should grant you an increase in rank.
Perhaps they believe that - in an ideal world, team cohesion should be baseline for everyone - and that the only difference therein between players of rank should be personal skill.
It could also be because in the previous mention of team cohesion versus personal skill, some players may have incredible personal skill but may lack in their own ability to work with their team, and may find themselves frustrated in facing an enemy team who can deal with one extremely skilled player among a team of average players through coordination, negating the 'carry' phenomena. You can argue that a coordinated enemy team is annoying to face for someone who is used to relying on themselves, but in the reverse it's just as disheartening for a team to lose a game because one opponent managed to snowball and carry, and the interaction between your team and the rest of the enemy team ends up having zero significance.
And then there are the players who are incredibly toxic or antagonistic, those who would be rebuked by the community at large by nature of their behavior, and thus cannot push themselves towards a system that promotes teamwork and camaraderie due to their own issues, and thus can only find company with others like them. The previous solo queue system was a boon because cohesion was limited among teams by nature of the system, and their behavior made little difference in the long run for ranked progression as long as personal skill was present and their behavior did not result in disciplinary action, something that is now a detriment in a system where large premade groups are possible, and their attitude would hurt their chances to play consistently with people who work well together.
So there are people who have all of a sudden found themselves in a new game, where the rules are the same but the people you play with and against can now be more than just strangers outside of a ranked 5v5 setting (or 3v3 for Twisted Treeline), and they find that their 'every man for himself' mentality is no longer wholly supported. Suddenly their ability to carry games by themselves can be stonewalled by a team that - while weaker than you individually - know together how to deal with you when you try to go Rambo and save the day by yourself without the input of your own team. All of a sudden, your tendency to stir trouble, flame your teammates, and ragequit when things don't go your way, doesn't just bring you closer to getting disciplined by Riot, now you find that nobody wants to keep you as a teammate when trying to form a team.
The game has changed and hurt some people, not by making it so that they can't play, but now their playstyle has negatives as well as positives that the previous solo queue system covered.
I believe wholeheartedly that dynamic queue should be adjusted so that it doesn't hurt solo players simply because they aren't on a team, but solo players can learn to be good teammates even with complete strangers and they will rise regardless of how things go (team that rise together will in turn rank up and eventually face those who are either their equal as a cohesive team, or better than them on average as individual players but less coordinated overall).
The death of solo queue truly hurts the people who can't work together with others in a team based game, and unless solo queue returns in some form, they will have to learn to play better with others and live in a world where they can lose to an inferior team with better coordination.