Why does Teddy think Elaine is Alice?

Teddy claims Elaine is his daughter, Alice Roosevelt: Alice was known as a wild child and one who shunned the norms concerning how young ladies “should” have acted. She became a fashion icon whose Blue dress touched off a national craze, the colour became known as Alice Blue, and inspired a popular song Alice Blue Gown President Roosevelt once said “I can either run this country or attend to Alice, but I cannot possibly do both”