My stance rests on three legs. Common sense, referring to experts, and caution.
Let's start with common sense. Viruses spread from person to person. The less people mingle, the slower the spread is. Even if eventually everyone gets infected at some point, by slowing down the spread we can flatten the curve and prevent unbearable pressure on the health-care system.
Referring to experts is a nice name for appealing to authority. This is admittedly the worst way to support an opinion, but it's also one we have to do every day. No one can be informed about everything, so you have to outsource your belief verifications to experts in almost every field of life. If epidemiologists and economists say lockdowns are a necessary evil, then I, being none of them, accept their word at face value.
Call me naive, but I also believe that politicians listen to experts. Call me cynical, but I also believe that they always keep their own interest in mind. Almost all Western governments have implemented some form of lockdown, and I don't think it can be fully ascribed to groupthink. Lockdowns cause severe economic damage which always hurts political leaders. If they chose to shut down their economies, they did it because they thought the alternative for them would be even worse. Groupthink is not a satisfying explanation for that, especially considering that no country followed the same pattern. Sweden has chosen not to implement lockdowns at all. Russia made a panicky U-turn after the short and typical strong-man stunt of disparaging the Western panic. Israel, whose people are not prone to public anxiety of imaginary dangers, locked down, too.
To address the caution part, every public measure either under- or overaddresses the problem it aims to solve. Shutting down the economy might be an overreaction, but with an unknown and deadly virus, that's exactly what I'd want the government to choose over the opposite. I prefer unnecessary economic damage to an unnecessary death toll. When the world-wide lockdowns were introduced, the mortality rate was estimated in the range of 0.5 and 6%. Italy had around 10%. It wasn't known which age groups are in danger, whether kids can contract the virus or spread it, what's the reproduction number, and many other factors. Today, as far as I know, the mortality rate is generally thought to be around 0.6% - which is still 6 times deadlier than the common flu -, and kids are not really at risk. These are good news, but they could have turned out very differently. If the mortality rate were around 10% among children and not among octogenarians, every family would live in their basement behind boarded-up windows. I would certainly do.
These are my arguments. Let's see the opposite side.
"This is an unacceptable invasion into our personal liberty"
Let's start with the libertarian argument which is the easiest to brush aside. Some oppose lockdowns on the ground of the perceived violation of personal liberty. This is nonsense. No one has the freedom to harm others, and that is exactly what a person infecting others does - even if unwittingly. If you subscribe to this reasoning, how would you make the case against anti-vaxxers?
The most common argument is that "the whole thing is blown waaay over, maaan". There are many sub-strains of this.
"This is just like a severe version of the flu"
Tens of thousands a year die in flu in America and no one thinks we should kill the economy because of it. That argument might have been worth considering months ago, but not anymore. The average yearly death toll of the seasonal flu is 10-60,000. COVID-19 has killed 180,000 so far and still counting. All of this while mandatory social distancing was put in place. The number would be much higher without it. The second wave has just started, and no one knows how long it will last or will there be another one.
"The numbers are unreliable, they count everything as COVID-death"
To invalidate the previous point, one has to put the numbers in question. So the next most popular argument is that the data are not reliable. Deaths are habitually ascribed to COVID even when the person would have died anyway from other causes (probably to serve the nefarious plans of...who actually?). That is surely true in many cases, but we have other statistics to look at that neatly eliminate the problem above. This is the number of excess deaths, that is, the increase in the number of deaths compared with the statistical average of the previous years. In America, it is over 200,000, which is even higher than the official number of COVID-related deaths. In the UK it's 65,000 against the official COVID fatalities of 40,000.
"The cure is worse than the disease"
Maybe the deaths are real. But I've heard from multiple sources that the self-inflicted economic damage leads to more misery in the long term than the virus would have done. This is something that's hard to argue both for or against. In ten years, when all the consequences have played out, we can have a pro- and con list, and even then we will need to resort to counterfactuals as the bases of comparison. As for now, many critics commit the mistake of comparing the grim reality to the normal state of affairs. The damage the shutdowns cause should be measured not against last year's GDP data, but against the alternative reality of COVID without mandatory social distancing. Sweden has shown what could happen without a lockdown. Its quarterly GDP fell by 8%. The EU average is 12%, Germany 10%, and Switzerland also 8%. They haven't avoided much of economic damage but lost 5-10 times as many lives per capita than Finland, Norway, or Denmark. Every country is unique in many relevant ways (population density, age distribution, cultural norms, international connectedness, the time and severity of the first outbreak, etc), but Sweden can't be that different from the average of its direct neighbors.
That was it. As a parting message, I offer my favorite line of reasoning, which is a kind of reversed argumentum ad verecundiam fallacy. Listening to people with a history of good judgment is a good strategy, but there is another useful one. It is listening to idiots and tyrants, and firmly taking the opposite view. Who were the loudest opponents of the mainstream reaction? First the Russians who never cared about their citizens' well-being. Then the Belarus dictator, Lukashenko, who claimed that the best cure for COVID is drinking vodka and driving tractor. The president of Turkmenistan who in his country simply banned even the discussion of the topic. The Brazil right-wing president, Bolsonaro, who said if he got infected, he would just shrug it off due to his athletic youth. Donald Trump - no explanation required. Right-wing media almost everywhere. Fox News treated it for weeks as a Democrat-hoax, then even now as the normal flu - so what's the fuss about? The UK government, which is neither malign nor completely moronic, but has shown that they prioritize their personal interests over their citizens'.
It wouldn't survive strict scientific scrutiny, but as a rule of thumb, it is pretty reliable. When murderous dictators, crackpots, conspiracy theorists, plain morons, and well-known opportunists all tell you the same thing, it's a good sign to place your bets elsewhere.