Killing someone out of hate is an ideological goal.

In most cases, no. All hate is not ideological hate, and most killings are not ideological either. Most of the violence we see in the world is due to people’s personal relationships with each other, or are the result of some spontaneous fight.

The problem with what you’re doing here is you’re diluting the meaning of the word “terrorism”. You wrote out the definition, but you don’t seem to understand it. The key element is that terrorism is not just instilling fear, but using that fear to obtain political or ideological goals.

If instilling fear is sufficient to make someone a terrorist, any violent criminal or anyone threatening others becomes a terrorist, and the word loses its meaning.