Silver was the poor man's money. Silver miners were finding lots, and exchanging it at a fixed rate. Naturally, the bankers didn't like that, since they were forced to pay the inflated rate for the newly, more abundant metal. So Bryan took the populist position, while McKinley took the more conservative, and banker approved, line.

I don't know McKinley's reason for this. Maybe he just really like sound money, and wanted to stick with tradition.