Is there any reason why the Criminal background in 5th edition D&D does not give you the bonus language of Thieves' Cant? With an admittedly limited understanding of the criminal world, I still know that thieves are not the only members of a criminal organization. Though the Rogue does have three different paths, none of them are the equivalent of a fighter or barbarian in terms of "muscle" for a thieves guild.
Thieves' cant is a fluff ability that will rarely if ever have a significant impact.* If you believe Criminal background should grant it, you won't break anything by modifying it. If you're really concerned with balancing the changes, consider that all basic backgrounds give a total of two tool proficiencies and languages, in any combination. Replace one of the tool proficiencies criminal background grants, and you're set.
There is no particular reason for the way it's written. While it's possible to speculate on the designers' intent, we're unlikely to ever know without their direct input.
* it's not just my speculation, here's a quote from Unearthed Arcana:
On the R&D team, any ability meant to convey flavor rather than a mechanical advantage is referred to as a ribbon—a thing that’s mostly for show. Thieves’ Cant is a great example of a ribbon ability, and Storm Guide also falls into this category.
It's not automatic because it's an unwarranted assumption that all criminals would automatically be thieves or have knowledge of the Cant.
Examples: A druid assassin could have the criminal background in that he uses wildshape to infiltrate areas so that he can get close to his targets. There is no need for a thieves cant there, and no real back story to support his having it, thus the criminal background automatically granting it doesn't make sense.
Second example: You're a monk with a criminal background who specializes in knocking out humanoid targets and then selling them. So you're a slaver. Again, no substantiation for knowing or having the Thieves Cant.
Backgrounds give you small bonuses. Having Thieves' Cant, Druidic, or other secret languages is a big deal. Secret languages don't come from backgrounds because the designers want to make sure that the game remains close to the game-balance they want, even if doing so causes the game to move further away from the setting they want. Thieves' Cant isn't worth much, as far as class features go, but it's still worth much, much more than a regular language.
Create a new background that justifies thieve's cant following the play balance of the current ones and ask your DM if you can use it in the game. The backgrounds are just example ones and obviously don't cover every possible one. However your DM should reject one that is to specific and could not be shared by other characters. Anything that specific should be gained by having to make difficult character choices about class etc. to add a bit of flavour - the most character defining traits in rpgs tend to be those caused by adversity.
Being a criminal does not mean that you have ever been under the tutelage of someone who would teach you thieve's cant, which is most often associated with ties to the Thieve's Guild(s) or other organised crime rings of the area (depending on setting etc). You might have been an enforcer for a criminal ring not of sufficient status to learn the "inner secrets", you might be a loner con artist, petty thug etc.