The CAP has two major "pillars". Under the first, direct support to farmers is mostly paid irrespective of the crops they grow or the animals they breed and therefore no specific payments are made for the breeding of bulls. Under the second pillar, EU support through rural development measures can be granted to holdings for a range of different purposes, e.g. in order to improve their competitiveness, independently of the final use of the agricultural product from the farm.
Much as it is sensitive in some countries of the EU, in others bullfighting is considered to be a cultural tradition and part of their regional heritage. Therefore the European Commission has no power to either stop it taking place or exclude it from the Common Agricultural Policy. A change of that nature would require a change to the Treaty on the Functioning of the EU, and would need to be agreed by all EU member states.