As of March 12th, the fatality rate of the coronavirus is about 0.5% overall and 0.2% until the age of 40 (graph), in which the latter number is about the same worldwide death rate as the normal flu. Moreover, the symptoms are also about the same as the normal flu, and 81% of the time the symptoms are only mild (Wu and McGoogan, 2020). However, even citizens who are not in the risk area and have no contact with older people seem to be away more concerned about getting the coronavirus than normal flu. Consequently, governments appear to be taking radical measures to not lose votes for doing nothing, but their vaccine (responses) may well be worse than the disease (COVID-19).
Switzerland has prohibited all gathering of more than 1000 people; Trump has ordered the stop of all flights from Europe; the country of El Salvador has prohibited all foreigners to get into the country and imposed a national quarantine (although it has no confirmed cases); Italy is closing all shops, except groceries and pharmacies. Initially, the government responses to the virus may be made sense because many people were panicking often after watching mainstream media (which has the goal of attracting viewers and making money, and not to spread the scientific truth). This panic was leading many people to cancel flights and hotel reservations, which is terrible for countries that have 10% of its GDP based on tourism, like several European countries (OECD).
On the other hand, responses now have possibly gone out of proportion. If you prohibit all foreigners to get into the country, the argument to take measures against the virus to protect the tourism industry no longer makes sense by definition. Closing borders also make little sense as trade is a huge part of most countries economy nowadays. For example, trade as a percentage of GDP in the US is 28, China is 38, El Salvador 78, Germany 89 (World Bank). Businesses are canceling meetings, sometimes putting workers on leave, cutting staff, or even going bankrupt. Stock prices reflect future economic expectations, so stock markets are obviously reacting. The head of the European Central Bank, Christine Lagarde, already said that the coronavirus can spark a recession like the 2008 Financial Crisis in Europe, which led to 260 thousand additional cancer-related deaths in OECD countries alone (Maruthappu et al 2016). And that's only from cancer. This 2008 Crisis's death estimation does not count any other disease or thousands of depressions and suicides that happen due to economic crises (e.g. Paul and Moser, 2009; Morris et al, 1994). Many lockdown supporters think that a near-complete economic shutdown would be saving lives as an exchange from economic losses. However, that is not exactly the case. By locking down a region the trade-off is saving lives now to kill people in the future as cancer, suicide, domestic violence, and heart diseases would all increase. Not to mention, the moral question of the value of lives. More specifically, is an elderly person's life worth the same as the life of a child? The average age of people killed by COVID-19 is around 80 years old, while an economic recession leads to the death of much younger people on average. Given the low fatality rate of COVID-19 among the majority of the population, it is even unclear if a severe economic recession would lead to fewer deaths than just letting the coronavirus spread without a general lockdown.
Moreover, COVID-19 may spread too easily to be contained in a world divided by international borders where countries can choose policies independently on how to fight the virus. This is especially true in emerging markets, where governments have less control over their societies and informal sectors are larger. Therefore, coronavirus may be out of any government or individual control. In the worst scenario, it may just become pandemic like the Spanish flu (which was much more deadly). Regardless of how many times you wash your hands or avoid contact, you may still get it someday, like the normal flu. Germany's head of state, Angela Merkel, just said that 70% of the German population may have to face the virus. In that scenario, efforts to stop the virus will at best "flatten the curve" and deeply hurt the economy. In a rational world, it could just make sense to remove the virus preventions among the low risk population that hurt the economy and let the COVID-19 spread while locking down only the high-risk individuals. It is possible to conceive that the human loss may be smaller in this scenario, all else equal.
Thus, how could so many people be potentially overreacting? Humans are frequently not rational as many Nobel Laureates have shown, such as Richard Thaler, Daniel Kahneman, Robert Shiller, and Elinor Ostrom. People are influenced by factors such as herd behavior and overconfidence. Even if you give them all the best scientific information in the world, people still often take the wrong decision.