down on someone—(coll.) expressing strong disapproval of smb.; reprimanding a person severely:
- “They’re down on her for some reason or other,” he told himself. “Angry, most likely, because she’s hung on to her boy.”
down to someone—being the responsibility of smb.; being incumbent upon a person:
- You need to be a good communicator to get your business vision across. Remember the success of your business is down to you.
Note: The expression is not antonymous in meaning to the phrase up to someone— = down to someone:
- The success of your business is up to you, your efforts and your commitment.