We are not told a lot about Friedrich´s family. We find out that he had a sister, Minna, who married an American and on her deathbed, she asked Fritz to take care of his nephews and raise them in America. It is not part of the canon, but I have read a couple of fanfics where Minna´s husband was an American journalist who abandoned his family and Minna was also quite possibly a journalist. This would explain why Friedrich does his best to look after the boys, wants to be a good role model and someone who never abandons them. Book does imply that Friedrich and Minna were very close. This is a common narrative pattern in Louisa May Alcott´s novels. In Work story of experience protagonist´s love interest, David has lost the connection with his sister and is filled with joy when he finds her. In Moods, the character of Geoffrey Moore takes care of his ill sister until she passes away. A devoted Little Women reader might even notice that in Greta Gerwig´s film Friedrich says it is hard to lose a sister.
In the 19th century, German immigrants were the second biggest group of immigrants in the US only surpassed by Irish immigrants. March family (and the Alcott´s in real life) were descendants of Irish immigrants. Between 1847–1855 German immigrants came to the US in large numbers. Many came in the hopes of a better way of life, others because of individual curiosity, economic hardships, political struggles or religious persecutions. Many escaped crop failure and famine. When we first meet Friedrich we find out that he has been living in New York for five years, which means that he arrived in 1860. In the early 1860s, main transportation across the Atlantic was made with sails and the trip could last one to three months. This would mean that Fritz would have arrived with a sailing ship that was designed for a cargo carrier. These ships were quite hazardous and the accommodations were small and dark. The second wave of German immigrants arrived at the end of the 1860s escaping the German wars.
Friedrich´s reasons for leaving his home country are family-related. There are a couple of occasions in Little Women that do give an impression that Fritz has faced oppression and discrimination and Jo does make a note to herself that he must have had a hard life. It is not a coincidence that Jo and Friedrich meet in New York of all places. Many of the German immigrants moved into the cities in the north, like New York, which already had established German communities. These communities were tight. When Friedrich comes to visit Jo in Concord the reader finds out that he has German friends there.