brouiller

To blur, scramble, or mix up — brouiller un signal, brouiller les idées — and, reflexively, se brouiller avec quelqu'un, to fall out or have a falling-out with someone.

• La pluie brouille la visibilité sur la route. — The rain is blurring visibility on the road.
• Il s'est brouillé avec son frère il y a des années. — He fell out with his brother years ago.
• Ces informations contradictoires brouillent le débat. — These conflicting reports are muddying the debate.

Se brouiller avec quelqu'un (to fall out with someone) is reflexive with avec — dropping the reflexive pronoun changes the meaning entirely, to simply 'blur/scramble' rather than 'have a falling-out.'

• expression "Brouiller les pistes" — A documented idiom (Expressio, L'Internaute), which emerged in the first half of the 20th century, meaning to lay false trails to throw pursuers — or the truth — off track.