Here's why:
* Ho-Oh is a Legendary Pokemon: It is a very rare and powerful Pokemon that typically appears in specific events or games.
* Shiny Gold is a fan-made ROM hack: It's not an official Pokemon game released by Nintendo. The developers of Shiny Gold choose which Pokemon appear in their game, and Ho-Oh isn't one of them.
If you want to catch Ho-Oh, you'll need to play a different Pokemon game where it's available, like Pokemon Gold, Silver, Crystal, or SoulSilver.