What should I tell my boss if he wants me to hand over root passwords to everyone in the office just cause there should be more than one person available to handle problems if I'm not available.

All these other people in the office have no experience with Linux or servers at alll and will fuck it up I know for sure.

run

Don't use the root account.

Give each user their own account and use sudo (much easier to revoke access when someone leaves or screws up then)

never never. Although it would seem to make things easier for workflow, there are reasons that these things are handled the way they are. Also you are saving your own ass, boss wont see the negative implications untill the systems have been compromized, and then it will have been your fault anyway because "you should have known" right?

Go over his head and explain the risk he is taking to his boss?

I'm with @itsnotmyfault, disable root altogether and use sudo. This is a much safer practice. Your boss is right though, if you get hit by a bus tomorrow, others should be able to do your job.

@ninjatini it's funny because that's exactly what he said

@ItsNotMyFault doesn't change the fact that they can raise hell with the access