Why do we keep giving people asylum when the United states is not a sanctuary?
Because we signed the post war UNHCR treaties that make us, along with many other nations, part of the global effort to end statelessness.
America signed the UN international asylum treaty on so are obligated by the law
The US is a signatory to multiple UN treaties requiring it.
It's an international law. And very few asylum seekers are granted asylum. Most are sent back home. https://ijrcenter.org/refugee-law/
People immigrated here from Europe exactly because they were seeking asylum and wanted a sanctuary where they could practice their own beliefs and live their lives how they saw fit. That's what drove most of the earliest immigration to what is now the United States.