In the context of the 16th century Protestant Reformation the Roman Catholic Church taught (and still teaches) that the Lord’s Supper is a divine sacrifice in which Jesus is offered in a bloodless manner. Rome teaches that Christ is “truly, really, and substantially contained in the propitious sacrament of the holy Eucharist under the appearance of those things which are perceptible to the senses” (Council of Trent, 13.1). The Reformers rejected this definition of the Lord’s Supper on biblical and exegetical grounds. For one example, here are Edward Leigh’s (d. 1677) ten reasons (summarized) for rejecting transubstantiation:
1) Christ would have to hold himself in his own hands and eat and drink his own flesh because, according to the Gospel accounts, he ate the supper with his disciples.
2) Christ would need two bodies, one broken and having the blood separated from the cup, and the other whole and having the blood in the body that holds the cup.
3) Christ’s blood would have been shed before his crucifixion.
4) His one body would have to be in a thousand places at once in order to facilitate the celebration of the supper in different locations.
5) A true body is finite and cannot be in multiple places at once.
6) Accidents would be without a subject, but Aristotle maintains that accidents are the very substance of a thing (cf. Aquinas, ‘Summa Theologica’ IaIIae, q. 90, art. 2).
7) The same thing would be and not be at the same time.
8) It is inhumane because no one but cannibals eats human flesh.
9) Our senses would be deceived because the sacrament looks like bread and wine but is not.
10) There is no change of the water in baptism, yet it too is a sign like the supper.
These reasons are why the Westminster Confession says that the doctrine of transubstantiation is repugnant not just to Scripture, but even to common sense and reason; transubstantiation overthrows the nature of the Sacrament and it also has been and is the cause of many superstitions and idolatries (WCF 29.4, 6).
For the above ten points of Leigh, see John Fesko, The Theology of the Westminster Standards. For the complete treatment by Leigh, see Body of Divinity, 8.9.