One, we want our government to be politically aggressive on a US Citizen's behalf, if the "crime" they commit is a civil right domestically.
Two, the danger to a US citizen in Mexican jails would easily violate the 8th amendment in multiple ways, including being held without bail.
Three, the spirit of the "no firearms" laws in Mexico were not violated. More than one American has accidentally done the same thing. Believe it or not, kids can make boneheaded mistakes, that yes they should pay for, but proportionally. There was no evidence he was trying to use the firearms or sell them.
Four, he is a US service member, who our government should absolutely make it a top priority to get transferred to US custody. Using our military as political pawns has to be strongly discouraged.
Five, it is political, as mentioned. Mexico has a massive inferiority complex, and takes any chance it has to show the United States that "we aren't the boss of them" like children. The local police and officials are corrupt, and probably sold his firearms already.
Eleventeen, after our government facilitated actual illegal firearms sales to Mexican drug cartels, some of which ended up killing countless Mexican citizens, and a US federal agent, you would think they would try to show some understanding of mistakes.