why did the british stay in the US after the revolutionary war?

The British didn't.  All Britons in America became Americans.  Anyone who would not pledge allegiance to the United States of America but instead remained loyal to the British Crown—"Loyalists," they were called—were systematically expelled northward into what would become Canada.  That led to a high concentration of Loyalists north of the new United States and their reprisal, which with the support of the British Crown and the British military and under the auspices of creating an independent country for Native Americans west of the new United States of America but ulteriorly to thwart its proclamation of Manifest Destiny as well as get revenge, would become known as the War of 1812.

EVERYONE was British in what later became the USA before the Revolutionary war.  If they had all left, the country would have emptied out.

In fact, about 1/4 of the people were Loyalist, many of whom moved to the northern colonies, that would later become Canada.

They didn't.

They stayed in North America, because not all the British territories in North America joined in the Revolution - only those included in the Thirteen Colonies.

Everything else remained under British control.

In some cases (like Canada) they're functionally still here.  In others, territory was ceded to the U.S. after the War of 1812, or at various times as a result of treaties, like the Oregon Treaty of 1846.

They forgot where they berthed their ships. One group said they were harboured at New York. Another said no, they were tied up in Boston. So they split up, to search. Unfortunately, they weren't too bright, got lost and ended up going west to the Californian coast and south down to the Gulf of Mexico, and eventually they became the Americans who, today, vote for Donald Trump. Hope this helped.