The formal structure of a fallacious argument affirming a disjunct looks like this:
A or B,
Therefore not B.
This is not a valid form of argument, yet it is a commonly utilized fallacy.
Let’s look at two examples often inferred from John 10.
John 10:11 reads, “I am the good shepherd; the good shepherd lays down His life for the sheep.”
The passage can be formalized with an inferred disjunct as follows:
(A) The good shepherd lays down His life for the sheep (or B) The good shepherd lays down his life for those who are not sheep
(A) The good shepherd lays down His life for the sheep
Therefore, not (B) The good shepherd lays down his life for those who are not sheep
This is a fallacious argument that attempts to validate limited atonement, but John 10:11 makes no statement about who He didn’t die for, only about who He did die for. In other words, we can make no positive assertion form John 10:11 that Christ didn’t die for someone because that someone is not one of His sheep. Passages like 1 John 2:2 and 1 Timothy 4:10 shed more light on this issue, but John 10:11 is not a proof text for limited atonement.
John 10:17 reads, “For this reason the Father loves Me, because I lay down My life so that I may take it again.” The passage can also be formalized with an inferred disjunct as follows:
(A) For this reason the Father loves Me, (or B) For other reasons the Father loves Me
(A) For this reason the Father loves Me,
Therefore, not (B) For other reasons the Father loves Me
In this passage, Jesus is not identifying all the reasons why the Father loves Him, He is only identifying one, but that is not indicative that there is only one (of course there may be only one, but this passage isn’t asserting that). Consequently, John 10:17 cannot be used to support that the Father’s love for the Son was conditional. Contexts like John 3:35, 5:20, 17:3-10, and Matthew 3:17 all help us to understand that love was an ongoing part of the eternal relationship between Father and Son.
Reading theology into a passage in order to support that particular theology is always exegetically problematic, and can also be problematic with respect to logic.