> Does a CEO improving his company market value by firing people have the same contribution to society as a paramedic saving a life, a nanny taking care of a baby so the parents can work or a teacher educating kids?
According to society's value system, as reflected by market pricing, I believe the answer is generally yes, the CEO is valued more.
The CEO is valued more because their work affects the company they lead as a whole and the work of many other people at the company - such as by determining what to work on, what initiatives to invest in strategically, or by obtaining funding for the company from investors. Poor decisions by the CEO can cause the entire company to fail; good decisions can create 100x as many jobs at the company, and increase its value by 100x.
It is more difficult for people to grasp the value of CEOs because their effect is spread out over a lot of people and abstract concepts like company success. It is easier to grasp the value of a nanny who spends time with your kids. But the fact that the nanny's work is much more concrete and obvious does not mean that it's more valuable. Consider: how much will you personally spend on a nanny? Would you spend 30-50% of your income on a fantastic nanny (the way that many people will spend that amount buying a house?) Most people don't value a nanny that much.
For a comparison, think about the effect that a good or bad president will have on the entire US. They can make a tremendous difference to the lives of hundreds of millions of people. A good CEO can do the same for their company, and all of their workers and investors. A bad CEO can do the opposite, and run the company into the ground.
Nannys and CEOs operate at entirely different scales. A CEO can destroy billions in value, or create billions in value. This is why companies and their boards and investors value good CEOs highly and pay them well. They want the best possible person for the job, and the best people demand high compensation.
There are also factors of supply and demand to consider. Most adult humans are intrinsically equipped to be nannies - to care for children. We're evolved to do it. No specific qualifications are necessary beyond not being a shitty or unreliable person. By comparison, not many people are equipped to be an effective CEO of a large, medium, or even small company. Thus, nannies earn less because there is a large supply of people who can act as nannies (almost the entire adult population), and a substantially smaller supply of effective CEOs. They need intelligence, drive, education, charisma, leadership capability, experience, vision, and other qualities.
Regarding your specific point about CEOs cutting jobs, sometimes that needs to happen. Lines of business don't always remain profitable. Sometimes a company needs to shut down unprofitable business units entirely, and exit the business. Sometimes a company needs to lay off workers and find a different approach to remain profitable.
Sometimes a job that was done by humans before will be automated tomorrow. For example, the company Hostess that makes Twinkies used to employ 22,000 workers. The company went bankrupt, and people bought its ashes and restarted it. The new hostess now heavily takes advantage of automation and employs only 1,170 people. (1)
A lot of people got laid off in that transition. The layoffs were also necessary for the company to continue at all; otherwise it would have gone under for good. They had a non-viable economic model for producing their baked goods. The leaders in charge of the transition took the only reasonable action (in hindsight) to prevent the company from cratering. (1)
CEOs are the people in charge of making the best decision for their stakeholders in really tough circumstances. Sometimes layoffs are the best possible outcome among many worse outcomes. No CEO would prefer to lay off their people - it's a horrible thing to have to do - but when the company is in dire financial straights, sometimes there is no better alternative.
(1) https://www.washingtonpost.com/news/business/wp/2016/07/05/w...