Signing up for the THG quota is, of course, voluntary. However, if you do not sign up for the THG quota and do not sell it to petroleum companies, the government can participate in quota trading on your behalf. Thus, not participating in quota trading does not hurt the petroleum companies.
The basic idea of the THG quota is that companies that put CO₂ emitting fuels on the market will have to pay financially for the damage they cause, and the cost of doing so will increase year after year. These rising costs will presumably be passed on more and more to consumer prices for gasoline and diesel in the future. This should ultimately lead to a switch to vehicles that have less to no impact on the environment. The THG quota alone will certainly not solve the climate crisis but it is one of many instruments to promote a transition to e-mobility.