For me, I think any confussion I had was with the actual words of Christ. Christ said," whoever eats my flesh and drinks my blood", implying both as necessary. I do understand what you are saying though…
The clue is in the Doctrine of Transubstantiation.
What is present before us is the Substance of Christ, His Body, Blood, Soul and Divinity.
Christ is living, His Flesh is alive, and His Blood courses through His veins. ’
What our senses experience is different from the actuality.
Our senses see Bread and Wine, while the reality is a whole living person.
In consuming this living person (Christ) we eat His Flesh and drink His Blood. That is the definiton of ‘drinking’, is it not, to consume that which is liquid.
Our senses do not experiece the reality of what we are doing, but the reality is there, nonetheless.
We eat His Flesh, we drink His Blood, even if our senses tell us otherwise. Just as our sense of sight sees only Bread, when the reality is different.
That is the nature of Transubstantiation. Our senses do not tell us what the reality is. But the reality is there nonetheless.
In addition, as Tantum mentioned. the Last Supper narrative gives commands that only apply to clergy ( the Apostles were clergy, bishops, at that point).
The Church understands that the instruction to “Do this in memory of me” is an instruction to offer the Sacrifice of the Eucharist, which can only be done by priests and bishops. That instruction does not apply to us.
That is one of the reasons that the priest must always consume both species, but we cannot assume that the instruction to eat and drink, in the physical sense, must apply to the laity.
That position was condemned as the part of the heresy of Utraquism, with the true teaching of the Church articulated at Trent (see ProVobis’ post above)