Why do humans get sad at specific patterns in music? Why does this sometimes happen even in major keys?

This depends on the effective implementation of all music parameters - tempo, meter, rhythm, melody, harmony, orchestration.  Listen to Schumann, Mahler, Brahms - doubtless others. Many of the above will evoke longing, loss, regret with the use of half-step resolutions, mainly plagal.  That is one shot in the dark / and overly simplified. And once you consider lyrics - another whole game.