Why can anyone administer baptism?
The short answer
Because baptism is ordinarily necessary for salvation. Priests and deacons are the ordinary ministers, but in life-or-death situations when none is available, anyone — Catholic, non-Catholic, non-Christian or non-believer — may baptize, using the correct manner and with the intention to baptize.
Ordinary ministers
Priests and deacons are the ones ordinarily expected to baptize.
In necessity, anyone
Because baptism is ordinarily necessary for salvation (John 3:5; CCC 1257), in life-or-death situations where no priest or deacon is available, anyone — Catholics, non-Catholics, non-Christians, even non-theists — may baptize, provided they do it in the correct manner and with the intention to baptize.