Not every thing the government does is good, and not everything it does is bad. I see the vaccine mandate as a mixed bag. Biden was reluctant to push for this; even some progressives are concerned about the government's growing footprint now.
Biden wants you to get vaccinated. He wants the pandemic to end during his first term in office. Biden doesn't really want to force you to do it, because he needs to keep his approval ratings up if he wants to get re-elected.
Your boss wants you to get vaccinated. He wants you to not get sick and not make your coworkers sick. Your boss wouldn't mind forcing you to get vaccinated, but he doesn't want to get sued and he doesn't want you to collect unemployment if he has to fire you.
So the Biden Administration and Corporate America came up with a plan. The mandate will "make" companies do what they want to do anyway: fire people for not getting vaccinated. But with the mandate in place, terminated workers will not have any legal recourse. When you try to fight the Man, the Man always wins.
People like to ask "Why does the vaccine have to be political?" Anytime the government is involved, it's political. Many Trump supporters are upset that Trump isn't getting credit for Operation Warp Speed. They want to boycott the vaccine out of sheer spite.
But if you care about politics, you need to realize that COVID-19 has a fatality rate that is greater than 1%. Elections are often decided by less than 1 percentage point. So let's you have a district with 100,000 Democratic voters and 100,000 Republican voters. All the Democrats get vaccinated. Let's say half the Republicans get vaccinated. Let's say 10% of those unvaccinated Republicans get sick. So that 5000 patients. One percent of them die. So now this district has 100,000 Democrats and 99,950 Republicans. Now, that might not sound like much of an advantage, especially since Democrats tend to have a lower turnout rate. But spread that across 435 Congressional Districts, and the GOP is going to struggle to take back the House.
So next year, when Democrats increase their control of Congress and become able to pass any laws they want, are you going to blame Biden for tricking you out of getting vaccinated?