If you look at the age of consent laws internationally, the US at the time wasn't much of an outlier.

https://chnm.gmu.edu/cyh/case-studies/230?section=primarysources&source=24

In 1880 in Denmark it was 12, Portugal 12, Russia 10. Even England and Wales during the Victorian period up until 1875 had an age of consent of 12 at a time when female puberty didn't occur until about 14-18. The differences in ages of puberty may be due to a poorer diet back then as well as that today we routinely ingest chemicals which are very similar to female hormones called xenoestrogens such as PCBs which were used as a refrigerant and a coolant, banned in 1979 but still present in the environment and drinking water. Medics and scientists aren't sure of the reasons and have numerous competing theories.

The first age of consent laws at least in the West was in England in 1275, where it was set at 12 and it was a more serious offence under the age of 10 from 1576. However most of the English colonies in what would become the USA decided to adopt the age of 10 to be the legal minimum.

Most of mainland Europe didn't start to introduce an age of consent until the 1800s with the Napoleonic code.

British suffragettes campaigning against child prostitution managed to increase the age of consent to 13 in 1875 and in 1885 to 16. There had been a problem particularly in London where girls once they entered into a brothel, were considered to be "always willing". So a brothel keeper might entice them in by offering them sweets or looking for girls who had just arrived from the country and had been sent by their families to seek work and were befriended by the brothel keepers or other prostitutes.

By about 1920 all US states had followed suite and the age of consent varied from 16-18.

The problems in defining "the right age" seems to have largely been based on differing ideas of when female puberty took place and how harmful it was to have an early pregnancy. In the early Victorian period and before the age of consent only applied to females, boys could legally have sex whenever they wanted and male homosexuality was either not legally recognised or completely illegal at any age. Technically a lesbian age of consent wasn't introduced into the UK until 2001 and females before that could have sex at any age. Although it could have been dealt with as a sexual assault.

https://chnm.gmu.edu/cyh/case-studies/230

Edit: minor grammar problem.

When did the legal age of consent come into being?