Fear and anger are generally distinct emotions. You can have one without the other. Many of the same pathways are active with fear that are active with an anger in your mind, mechanically speaking. You can have anger without fear though.

I see a lot of people can conflict the two, but they are distinct as label labels and mechanical processes in the mind. Anger surfaces when there is someone to blame. Or something to blame. Something you can pin the emotional and surge on.

For your hypothesis above to be true, you generally need some sort of risk involved for fear to be the actual emotion. Anger can appear with zero fear and simply something blocking your way.

So I’m just not sure that I really agree on anger needing fear. There are plenty of situations where it doesn’t hold.