"I hate them too, even more than you do, and my hatred almost cost your life and the lives of millions of vampires. If Axel had not insisted that I stop the transformation, you would be out there by now, killing every vampire you come in contact with, irrespective of whether they are guilty or innocent, old or young.
I still hate them, but this time, I want to channel my anger and aggression toward the particular ones who caused me pain, instead of the entire race. I have lost a lot of things and passed through unnecessary pain because I closed my heart to the entire race. I wouldn't want you to do the same.
Axel is not part of the conspiracy to wipe out your family, so you shouldn't channel your anger at him. Your anger should be channeled to the specific people who had a hand in your misfortune.