哥 = 可 + 可, the same element written twice and stacked vertically. The lower 可 sits beneath the upper one, so the glyph reads like an echo: one breath of sound returned a second time. Each 可 already contains a 口 (mouth), which is why the official radical of the whole character is 口.

可 began as a phonetic loan. In the seal script it depicts a curved breath rising past a mouth, and it was borrowed first to write the sound now heard in 歌 (gē, to sing). Stack two of them and you get the older written form of that song-sound. For a long stretch 哥 was simply a way of writing what we now spell 歌, the act of chanting or singing, before 歌 took on its own 欠 (gaping mouth) signific and split off.

The kinship sense arrived later and won. By the Tang dynasty 哥 had been pulled into spoken address for an older male, and the doubling fit the use: a sound you call out, repeated, the way a child calls 哥哥 (gēge) across a courtyard. The character that once stored a song now stores the warmest title in the household.

Japanese keeps the older trail visible. 哥 survives there chiefly inside 哥薩克 and a handful of literary spellings, while everyday "elder brother" went to 兄. Mandarin took the opposite road and let the doubled 可 own the family.

哥 reaches far outside blood kinship. Chinese address strangers as relatives constantly, and a young man slightly older than you is a 哥 by courtesy. Attach it to a surname, 王哥 (Wáng gē), and you have a warm, deferential way to call a coworker. Attach it to a quality, 帅哥 (shuàigē), and you have a compliment you can shout across a street.

Picture a younger child standing at the bottom of a stairwell, calling up: 哥! 哥! The cry goes out once, and a second time, an echo. That doubled call is the glyph: two 可 stacked one above the other, the lower one answering the upper, the small 口 mouth on each one open and sounding.

Now let the echo widen. The same call climbs out of the stairwell and into the street, where any older boy answers to it: the handsome stranger becomes 帅哥, the man behind the counter becomes 王哥, the leader of the pack becomes 大哥. Every one of these is the same doubled cry aimed at a wider circle. 哥 is the sound you send upward to someone older, repeated until it lands.