Heres my take on the rivalry for what it is worth:
When Everton were struggling with relegation, Liverpool won the treble. Therefore they were superior, as a result it didnt matter what we done.
When Everton started doing better under moyes, Liverpool won the Booker T title. 5 TIMES SUCKA'S. As a result what we done didnt matter.
When Everton started pushing for a top four place, Liverpool were there already. What Everton done didnt matter.
For all the above when Everton were doing well, Liverpool didnt care what we were doing because they were doing better.
Now Everton are fighting for the same aims, top four, fa cup, european success, they hate us because they know that there is a possibility, as slim as it might be, that Everton may win a Cup before them. It's like if your a millionaire with a bentley, you dont care if your neighbour gets a BMW. My car is still better. If you lose everything and they buy a Bentley whilst your forced to buy a BMW, you will feel abit of hate towards them or jealousy whatever you want to call it.
They will always rub it in our faces for being in their shadows while the going is good, yet they hate their manchester neighbour rubbing it into their faces that they have had more recent glory.
Whilst we appear bitter and they are a gift from god, imagine if we done a Man City and started acheiving the aims they once acheived before they were able to do it again. The bitterness or VENOM they show signs of now will be intensified tenfold. For now we simply laugh at them because they cant understand how silly they look slating us when United slate them for being inferior. Hypocrisy is immense.
Let them be people.