The meaning of all the Firstborn mitzvos we have is well-known. It is a group of Mitzvos that reinforce our connection with Makas Bechoros, the Plague of the Firstborn, which is what led to Yetzias Mitzrayim, our national founding moment.
A bechor is what turns a living being into a parent.
It is the first moment of another generation.
It is the second “dor” in the well-known phrase “L’Dor Va’Dor”.
It is the cure to the Death Decree issued in Gan Eden, because perpetuation is the very cancellation of mortality.
All signs of immortality belong to God. He made his claim on them.
The bechor class of an immoral society perpetuates the immorality and death.
Killing them in Makas Bechoros is Hashem telling Mitzrayim: How dare you use the symbol for immortality to perpetuate your immorality. It’s as obscene as bludgeoning someone to death with the Philosopher’s Stone.
So Hashem reclaimed the birthright for Himself. What he takes He gives to His servants. Thus, the Cohanim (and Leviim according to Parshas B’haalosecha) are entrusted with the firstborn mark.