The angry bit as pointed out is a 19 in 20 chance, so it is possible to get the angry message many *many* times before starting the tame. It is after you have passed this "angry" check that your skill comes into play as to whether or not the tame is successful.
I set the critter I want to tame as my last target, then I have my F12 key set to Use Skill Animal Taming, Last Target (in 2D client). I run to the critter and hold down the key until the tame starts whilst remaining a couple of steps ahead. The 'You seem to anger the beast' message does not count against the skill timer so you can immediately start the next tame attempt. Once you get the 'starting to tame' message, let go of your macro key and focus on staying ahead of the critter. If you fail, stay close and hold the macro key down again.
If you are scrolled beyond 110 then throw on some +taming skill jewellry for a better chance! (assuming that still works?)
Cheers!
Tukaran