Why Antenna gain is not power creation, it is power redistribution. An antenna focuses the same transmitter output into a narrower pattern, so the signal in the favored direction is stronger than it would be from a reference antenna such as an isotropic radiator (dBi) or a half-wave dipole (dBd). Gain is always quoted relative to that reference and in a specified direction, and whatever is gained in one direction is lost in others.
Watch out The idea that gain adds power to the transmitter is the classic trap: a passive antenna has no amplifier, it only concentrates the power it is already fed. Impedance has nothing to do with gain, it is a matching issue.
Gain is focus, not free watts. A flashlight reflector, not a bigger battery.