the usage of "invite"

I read something rare in the Longman Dictionary:

The word “invite” is not used when someone is actually inviting, it is only used in later remarks. We may say “Would you like to come to the party?” and then tell someone else “I have invited …”.

It seems never mentioned in English class from Junior Grade 1 to Senior Grade 3. Today, my current teacher corrected the usage, saying “If it is not a party, you can use ‘invite’ here.”

I’m completely puzzled now. Would anyone like to explain it? Why is party so special?

Hi Mr Takashiro,

Maybe I didn’t quite get it, but let me show you some examples:

  1. I’d like to invite you to a party this weekend.
  2. Who would invite you to a party?
  3. I wanted to invite you to a party.
  4. I have come to invite you to a party.

They all sound perfectly fine to me.