The ancients climbing mountains was not just a matter of writing poems. Climbing stairs was a sad thing in the eyes of the ancients. Many poems say that "the east wind blew in the small building last night" and "I went to the west building alone without words" all convey sad feelings.
Here, falling in love with stairs means that they go upstairs to write sentimental poems and find feelings, and write new words. Later, when they really feel sad, they don't have to go upstairs, so they say, "The weather is cool and autumn is fine."