Clearly the verse doesn't say he ate them which would imply he ate both. It is true what you say, and for those Christians who believe the Bible to be someway the dictated word of God, then they are left with this problem of how Jesus, be he prophet or God, could lower himself to eat the flesh of a dead animal. New members will not be aware that I do not believe the Bible to be the word of God. I know for a fact that till the time of Constantine, there were bibles used by large numbers of Christians that supported vegetarianism. I believe the Oxford Dictionary of the Christian Church states that Constantine had 30 of these bible written up as a bases for his new version of Christianity.
Mankind is lustful after flesh be it for eating or sex.
Mankind seems driven by a madness, and I do not believe for any reason that Jesus would have followed this example of humanity. As I have never tired of showing the list, the early church father's writings are full of quotes that Jesus and his disciples were all vegetarian. Modern Christians who want to be part of the masses and buy their green mini-vans, take properity courses and make up justifications for not helping the poor can do so and they can cling to their Constintine Bible, but I for one will follow Jesus. There are not two original manuscripts of the Bible that agree. There is no such thing as an inerrant bible, there never has been.