There are several possible ways how current pandemic may turn into a civilizational collapse (which may be the first step of an extinction event, depending on the possibility of recovery). I will list below several putative ideas of how the pandemic could turn into a global collapse. Each of them, I guess, has lower than 1 per cent probability:
Inevitable reinfection. The virus has an ability to mutate inside the body causing deadlier reinfection later with the “personal strain"; If true, most infected will die in a few months. This is how feline peritonitis coronavirus kills.
New strain. The virus will mutate globally in a new strain, which will be deadlier, or more affect children, or better evade quarantine and sanitation.
New waves. The virus is mutating so quickly that the vaccine is not possible, and each year will be new waves of reinfections, with mortality of a few per cent each.
Famine. The virus could be contained, but only via global lockdown. The economy as we know it will collapse and eventually famine and other forms of shortages ensure. Alternatively, the virus is not that deadly, but social collapse will happen anyway as a combination of border controls, riots, civil wars.
Infertility. The virus causes long-term health effects for most survivors, like infertility, reduced lung capacity and brain damage. This gradually reduces human potential and civilisational productivity.
Once enough people have been infected and recovered, gaining immunity, the evolutionary pressures on a virus switch from "spread as fast as possible into new hosts" to "keep the current host alive and infectious long enough to encounter a host without immunity". Even though influenza periodically bypasses existing immunity, the evolutionary pressure towards lower mortality is still present most of the time. In particular, our actions to quarantine and isolate, if sufficiently widespread, will also put a lot of evolutionary pressure towards less-severe effects on SARS-CoV-2. All those mild and asymptomatic cases? Pretty soon those are going to be the most successful replication strategy, and the SARS-CoV-2 population as a whole will be pushed towards causing lower mortality.
There is still a chance we'll have repeated high-mortality waves, but one should note that coronaviruses and influenza viruses are not particularly closely related. Influenza seems to have about one mutation in its protein coat per replication, while as of Feb. 11th the 81 sequenced samples of SARS-CoV-2 had "at most seven mutations relative to a common ancestor". So I'm inferring that SARS-CoV-2 is less likely to be able to bypass existing immunity on a yearly basis. Influenza has a high mutation rate due to lacking RNA proofreading enzymes, so if SARS-CoV-2 has an RNA proofreading enzyme or hijacks host-cell proofreading enzymes I would also update towards a lower probability of repeated waves. Influenza is also unusual because it's composed of eight pieces of RNA, which makes it easy for different strains of influenza to swap genes when they infect the same cell at the same time. This is another major reason that influenza bypasses immunity so often. SARS-CoV-2 seems to have one 30,000 base-pair segment of RNA, so it can't do that trick either.
There are still a lot of unknowns, but so far there's no evidence I've heard of which has made me update towards SARS-CoV-2 being more likely to be able to bypass existing immunity than other coronaviruses, much less influenza.
There are several possible ways how current pandemic may turn into a civilizational collapse (which may be the first step of an extinction event, depending on the possibility of recovery). I will list below several putative ideas of how the pandemic could turn into a global collapse. Each of them, I guess, has lower than 1 per cent probability: