Why isn't the Eucharist of protestant churches considered valid by non-protestants? The Catholicism and Orthodox churches do not recognize the Eucharist of protestant churches. Why not?
As far as both Catholics and Orthodox are concerned, you need a validly ordained priest to confect the Eucharist.(see e.g. CCC, ¶1411) As far as they are concerned, none of the churches that originate from the Reformation period have what is required for a valid priesthood (i.e. bishops in unbroken tactile succession from the Apostles(see CCC, ¶1576)), so the Eucharist cannot be validly celebrated by these churches.

This may look uncharitable on the surface. In reality, the Catholics and Orthodox could not accept the validity of Protestant Eucharists without significantly altering their own doctrine.



On another related point, it's worth noting that Catholics and Orthodox do not even properly consider the Protestant churches "Churches" in the proper sense: they are referred to technically as "ecclesial communities" precisely because they have not preserved the sacramental priesthood and therefore the Eucharist:


  According to Catholic doctrine, these Communities do not enjoy apostolic succession in the sacrament of Orders, and are, therefore, deprived of a constitutive element of the Church. These ecclesial Communities which, specifically because of the absence of the sacramental priesthood, have not preserved the genuine and integral substance of the Eucharistic Mystery cannot, according to Catholic doctrine, be called “Churches” in the proper sense. Responses to some questions regarding certain aspects of the doctrine of the Church)