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Put Someone Down

If you “put someone down” it means that you say something mean or unkind to them for the purpose of hurting them. The phrase to “put someone down” is usually used when someone is intentionally trying to hurt another person’s feelings. So, putting someone down is NEVER nice.
Another example: “I don’t understand why Tusk is so mean to people. I think he only feels good when he puts other people down“

Headache

It’s when your head hurts. You already know how to say, “I have a headache“. That is the most common one.

BUT… You can also describe annoying things or people as “headaches“.

For example, you could say, “Watching TVN24 is such a headache.”

Or… “She’s so annoying. Talking to her is such a headache.”

Ideas from: http://www.speak-fluent-english.com/