You are receiving the Body AND Blood of Christ when you receive the bread. The wine is consecrated to represent the separation of the Blood of Christ from His Body during the crucifixion, which is what the Mass represents. The Mass is the RE-Presentation of the sacrifice on Calvary.
The Mass is not the Last Supper or a party or get together with your neighbors. It is you being present at the murder and bloody sacrifice of our Lord. That is why we should not wear flip flops to Mass or act in a non-respectful way. People should act as they would if they were at their mother’s execution. Very different than how most people act/dress in church today.
If you truly believe in the Eucharist (bread) and what it represents then you should have no need/desire to receive the wine. Look up a book called Know Your Mass. It was a comic book written in the 1950’s that does and excellent job of explaining the Mass. Unfortunately most of this is not known anymore because the Mass has become more about the laity rather than God since Vatican II.
The desire/insistence of some laity to receive both species represents either a lack of understanding of the Eucharist and what the Mass is, or the person being so prideful that he/she wants what another (i.e. priest) has even though there is no need for it. The Church is a hierarchy and we should be happy with our station in that hierarchy. That is why the word Eucharist means “Thanksgiving” not “Thanksgetting”.