Have a down on somebody/something
Definition 1 of 1
Pro Tip 1/3British Slang
This phrase is British slang and may not be understood by English speakers from other regions. 
When I said he had a down on the new policy, my American friend was confused.
Pro Tip 2/3Negative Nuance
The phrase expresses a strong, often inexplicable dislike for someone or something. 
She's had a down on that restaurant ever since she found a fly in her soup.
Pro Tip 3/3Emotional Weight
This idiom carries emotional weight and can seem harsh if used carelessly. 
Saying that he's always had a down on his rival might seem like he's holding a grudge.