He was an orphan

Henry McCarty was born in New York City to Irish Catholic parents, Catherine and Patrick McCarty. According to one theory, he was born on September 17, 1859, in New York City. On September 28, 1859, he was named "Patrick Henry McCarthy" at the Church of St. Peter. While his birth year has been confirmed as 1859, his exact birth date has been challenged as either September 17 or November 23 of that year. According to a letter from an administrator at Saint Peter's Church in Manhattan, the church has records proving McCarty was christened there on September 28, 1859. According to census data, his younger brother, Joseph McCarty, was born in 1863.

Catherine McCarty and her sons relocated to Indianapolis, Indiana, when her husband Patrick died, where she met William Henry Harrison Antrim. In 1870, the McCartys relocated to Wichita, Kansas, with Antrim. Catherine married Antrim on March 1, 1873, in the First Presbyterian Church in Santa Fe, New Mexico Territory, after moving a few years earlier; McCarty and his brother Joseph were witnesses to the event. Soon after, the family relocated from Santa Fe to Silver City, New Mexico, where Joseph McCarty adopted the surname Antrim. William Antrim abandoned the McCarty boys, leaving them orphans, shortly before McCarty's mother, Catherine, died of tuberculosis on September 16, 1874. Therefore, after his mother died, he became an orphan.