Because slang was seen as a vulgar way of speaking that was inappropriate for refined young women.

Slang - language, words, phrases invented by doctors and boxers, lawyers, thieves, sportsmen and whores, necessarily or purposely to convey their meaning secretly to each other

- From Slang - a Dictionary of the Turf, the Ring, the Chase, the Pit, of Bon-Ton and the Varieties of Life (1823)

Don't use slang. There is some slang that, according to Thackeray, is gentlemanly slang, and other slang that is vulgar. If one does not know the difference, let him avoid slang altogether and then he will be safe.

Don't use profane language. Don't multiply epithets and adjectives; don't be too fond of superlatives. Moderate your transports.

Don't use meaningless exclamations, such as "Oh, my!" "Oh, crackey!" etc.

- From Don't: A Manual of Mistakes & Improprieties More Or Less Prevalent in Conduct & Speech, by Oliver Bell Bunce (1884) - a handbook for those just entering the urban middle class

The idea that women should be more sensitive and refined than the men of their class due to innate biological characteristics arose in the late eighteenth century (as I discuss a bit in this previous answer), and by the 1860s, when Little Women was written and published, it was very well accepted. While slang could be looked down upon in a gentleman or lady's speech, it was especially disreputable coming from a woman without the education to know what was "gentlemanly slang" or who shouldn't be using gentlemanly slang in the first place.

While Louisa May Alcott's own views on the subject were rather more radical - she published many thrilling stories involving murders and deception, which would not generally be considered appropriate topics for women of her time and class, and critiqued the limits put on women by society - she was also writing didactically. Meg's role in the novel is to be the voice of middle-class women aspiring to be fashionable. Sometimes this imperils her own morality, such as when she dresses up at the Moffats' party or when she buys expensive silk for a dress, and at other times she's just used to note Jo's improperly masculine behavior. "Capital" is a positive adjective, that Jo could replace with something suitably soft and feminine like "wonderful" or "nice"; "Christopher Columbus" was an exclamation equivalent to "holy moley" or "jeepers" or something along those lines, which in addition to being slangy falls under the "meaningless" issue from Don't quoted above.