> Maybe because nobody successfully proved to these people (me included) that this sacrifice is useful.

It's not a matter of proof, it's a matter of weighing the cost of action vs the possible outcome. Just like insurance, there's a low cost of action (low continuous payments) to hedge against a possible large negative outcome. It's also worth noting that some types of insurance are mandated because people are bad at calculating risk in general, and when they fail, we as a society don't necessarily want that to have too extreme an outcome, so we have societal guards in place to help. Mandated insurance shifts the burden from society (taxes) back the the individual. We see this in health insurance, car insurance, home insurance, etc. Sometimes it depends on region (some localities requires fire/earthquake/flood, etc insurance).

> people who are at risk of dying can protect themselves even around sick people (wearing a mask, staying at home, washing hands, ...)

To clarify, wearing a mask, as recommended by most officials currently, is not about protecting oneself, but about protecting those around you in the case you are unknowingly contagious. It greatly reduces the spread of your contagion, it does not greatly reduce your chance of being infected unless you are using a high-grade mask very securely fastened such that all airflow is through the mask and not around it.

> so this is not your fault if they catch it

It very well may be your fault if someone catches it if you're contagious but ignoring recommendations about avoiding gatherings of people, or not wearing a mask, etc. They could literally catch it directly from you with little ability to block it. A sneeze can travel very far, yelling expels particles with more force, and direct contact with people or surfaces they touch shortly after and then may touch themselves or something else they touch after washing their hands is not something easily protected against.

> but you need to stop living your life.

This, right here is the crux of the issue. What is being asked for from people ranges from not working to curtailing social group gatherings and activities. The work portion is horrible, and life altering, and actual affects people living their lives. The group activities being classified as "living your life" is both a) relatively recent for the vast majority of the world, which did not have the free time or money to do such things on a regular basis decades ago, and b) shows a complete mismatch by people of what the need and what they like and want.

A vanishingly small number of people actually need to go to the gym (those in physical therapy that need certain equipment), and the others can get basic exercise at home or outside without anyone around. Nobody needs to go to a bar. That we classify these niceties as "living our life" is really just a shift of priorities of modern people in first world countries away from actually having to worry about survival. But this is a matter of survival, and those thought patterns are doing us real harm as a society during this crisis.

> It is not that people don't want to sacrifice, it is just that scarifying is the worst solution for everyone

No, it's that people are unwilling to separate simple and (relatively) easy sacrifices from hard sacrifices, and acting like they're all the same. Get food from restaurants, but limit or eliminate the in-restaurant eating/time (you don't have to order door-dash, just pick it up). You don't have to stop drinking, or talking to friends, but you shouldn't do those in person when avoidable.

Collectively, people stopping the non-essential gatherings such as gyms and bars will not only reduce the spread and save lives, if everyone did it we might get back to the point where the increase in cases was so low more optional services could reopen again, lessening the economic impact.

It's not about scarifying, it's about making people actually understand how this works, and how their actions actually play into this when carried out by massive amounts of people. And when it comes to bars and gyms and people being unwilling to change their habit, it is also a bit about people not wanting to sacrifice. In the grand scheme of things, those are fairly small changes to ask for, and if people can't even bother to do that, what hope is there that they'll follow through with other things?