Why is only the Body of Christ offered at a Catholic funeral and not the Blood?

Answer 1

The idea behind it is that a body can't come without the blood, the body can't be completely free from blood so the body is good enough. Many miracles including ones where blood sprays out of the Eucharist proves this.

In the Orthodox Church, they do give out both though.

Answer 2

Just to be perfectly clear, Catholic dogma has always been that Christ is completely present, Body and Blood, Soul and Divinity, under either and both species. In other words, if you receive the Body of Christ under the appearance of a "wafer" you are receiving the entire Body and Blood, Soul and Divinity of Our Blessed Lord Jesus Christ; the same would be true if you only received under the appearance of wine. That being said, most Bishops now ask that their priests to offer both species at all Masses, and this is commonly done, but not always. The Second Vatican Council asked for Holy Communion under both species to be extended to specific people on special occasions, for instance, at a wedding, or at a confirmation Mass, or a special Mass for a religious Order. That being said, it is up to the individual priest, and often times at a funeral, the majority present are not even Catholic, so the priest would have no way of judging how many in the congregation might want Holy Communion, etc. This is not a general rule, in my parish, unless it is the height of flu season, the Precious Blood is offered at all Masses, even funerals. At my previous parish, which was at the Cathedral in another diocese, Holy Communion under both species was only offered at Sunday Masses. Period.

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If I may make a personal observation, no one should receive Holy Communion who refers to the Precious Blood as the "wine," until they have been sufficiently educated and been to Confession.