Objection 1. It seems unlawful to receive the body of Christ without the blood. For Pope Gelasius says (cf. De Consecr. ii): "We have learned that some persons after taking only a portion of the sacred body, abstain from the chalice of the sacred blood. I know not for what superstitious motive they do this: therefore let them either receive the entire sacrament, or let them be withheld from the sacrament altogether." Therefore it is not lawful to receive the body of Christ without His blood.
Objection 2. Further, the eating of the body and the drinking of the blood are required for the perfection of this sacrament, as stated above (73, 2; 76, 2, ad 1). Consequently, if the body be taken without the blood, it will be an imperfect sacrament, which seems to savor of sacrilege; hence Pope Gelasius adds (cf. De Consecr. ii), "because the dividing of one and the same mystery cannot happen without a great sacrilege."
Objection 3. Further, this sacrament is celebrated in memory of our Lord's Passion, as stated above (73, 4,5; 74, 1), and is received for the health of soul. But the Passion is expressed in the blood rather than in the body; moreover, as stated above (Question 74, Article 1), the blood is offered for the health of the soul. Consequently, one ought to refrain from receiving the body rather than the blood. Therefore, such as approach this sacrament ought not to take Christ's body without His blood.
On the contrary, It is the custom of many churches for the body of Christ to be given to the communicant without His blood.
I answer that, Two points should be observed regarding the use of this sacrament, one on the part of the sacrament, the other on the part of the recipients; on the part of the sacrament it is proper for both the body and the blood to be received, since the perfection of the sacrament lies in both, and consequently, since it is the priest's duty both to consecrate and finish the sacrament, he ought on no account to receive Christ's body without the blood.
But on the part of the recipient the greatest reverence and caution are called for, lest anything happen which is unworthy of so great a mystery. Now this could especially happen in receiving the blood, for, if incautiously handled, it might easily be spilt. And because the multitude of the Christian people increased, in which there are old, young, and children, some of whom have not enough discretion to observe due caution in using this sacrament, on that account it is a prudent custom in some churches for the blood not to be offered to the reception of the people, but to be received by the priest alone.
Reply to Objection 1. Pope Gelasius is speaking of priests, who, as they consecrate the entire sacrament, ought to communicate in the entire sacrament. For, as we read in the (Twelfth) Council of Toledo, "What kind of a sacrifice is that, wherein not even the sacrificer is known to have a share?"
Reply to Objection 2. The perfection of this sacrament does not lie in the use of the faithful, but in the consecration of the matter. And hence there is nothing derogatory to the perfection of this sacrament; if the people receive the body without the blood, provided that the priest who consecrates receive both.
Reply to Objection 3. Our Lord's Passion is represented in the very consecration of this sacrament, in which the body ought not to be consecrated without the blood. But the body can be received by the people without the blood: nor is this detrimental to the sacrament. Because the priest both offers and consumes the blood on behalf of all; and Christ is fully contained under either species, as was shown above (Question 76, Article 2).
Source: Summa Theologica (New Advent)