To disconcert is to unsettle someone, make them feel confused and out of sorts. It's a mixture of to embarrass and to creep out.
Disconcert comes from the old French word disconcerter meaning confused, which is just how it feels. The prefix dis means "not" — it has a bad attitude and shows up in dismiss (not accept), dissonence (not harmonious), and disown (not own), among others. After dis comes concert from the word concerter "to bring together" (like at a concert!). If you disconcert someone, it’s like you dis them at a concert, and that person is not having fun. At all.