Milchin was determined to expose the man calling himself Kirin as a fraud and a liar. He had already discovery the real John Kirin had died in Indonesia four years previously, and he confronted MacLeod about why he wasn't talking, what he was hiding about the man.
He realized that there was some kind of bad blood between MacLeod and Kirin and had decided to stake out the dojo, "snoop around a little bit," until he could confront MacLeod. He broke into the building and searched MacLeod's office.
He was followed by Kirin's self nominated protector, Matthew, and shot to death.