Once again remember this fact:
Monsters do not have priority. None of them do. It is the player who has it. Without recreating the long discussion thread that stickied at the top of this forum, here's a short short version.
Priority gives you the player the right to use the effect of your monster that you just summoned successfully (aka wasn't negated with "Horn of Heaven" or "Solemn Judgment" before the opponent can respond to it.
So, if you summon "Black Luster Soldier:EotB" you can use his effect to remove a monster on your opponent's side of the field before he can respond with say "Torrential Tribute". Or if you summoned "Magical Scientist", you can pay 1000 to summon a fusion monster first.
Now, in the case of a monster like "Breaker the Magical Warrior", "Breaker's" effect activates automatically (the put a token on Breaker) and therefore your opponent can chain to that so in a sense your "priority" was automatically used (the same would be true for all monsters who have an automatic effect).
- Andrew
