The motivations of Free Grace Theology - essentially Salvation by faith alone, and Eternal Security in their most unqualified senses - are profoundly logical. They see certain statements in the Bible, and from those statements, make logical deductions in order to get to a sort of "minimal Soteriology".
In this process, a few assumptions are taken for granted by proponents of Free Grace Theology, and they are assumptions shared by basically all Christians:
The quintessential example of this kind of reasoning can be seen in analyzing how a typical Free Grace Christian treats the statement in Ephesians 2:8-9:
Ephesians 2:8-9
8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
9 Not of works, lest any man should boast.
From the above, they may reason in the following way:
And:
These arguments are reasonable within the context of Ephesians chapter 2. They take the statement very seriously, and assume that the author would not say something which was in reality, rather meaningless, or nonsensical. And, since they assume that the New Testament is consistent with itself, the rest of the New Testament - regardless of what else it appears to teach on the topic of Salvation - must in reality comport with the fact that Salvation is a free gift, obtained by faith, in distinction from good works.
Similar chains of reasoning could be shown with passages like John 4:10-14, 5:24, 6:47, Romans 3:20-24 (the namesake of "Free Grace Theology"), Romans 4:5, and so on. These are all passages in which a reasonable person, assuming no duplicity on behalf of the authors, may easily come away believing in something like Free Grace Theology. Then, once this base is established in the mind of a person, any attempt to teach a Soteriology which involves good works is seen as an attack on the purity of the Gospel.
The reality of the New Testament is that it is a fallible compilation of works by disparate groups, and those groups actually taught incongruent theology - incongruent both internally (contradicting either themselves, or sound logic), and also incongruent with the theologies of the other early groups.
So, not only do many authors, taken within the context of their own writings, arguably teach a very clear-cut works-based justification (e.g. Matthew 5:17-30, 7:13-23, 10:32-33, 18:6-9, 19:16-30, 24:45-51, 25:14-30, 25:31-46, Hebrews 3:6, 3:14, 4:1-11, 5:9, 6:4-8), it is also the case that assuming that an individual author will be internally consistent, or logical, or consistent with other writers in the corpus, is badly misguided. There is no reason, apart from perpetuating the assumptions of early Christians - who all would have considered Free Grace Christians heretics - to assume the text of the New Testament is divinely inspired by God, or consistent with itself.
So, it may in fact be true that interpreting Matthew in an arguably straightforward way contradicts Ephesians 2:8-9. But, unfortunately for Free Grace Christians, it may just be true that Matthew contradicts the author of Ephesians. Likewise, it may be that Ephesians 2:8-9, taken most directly, teaches the tenets of Free Grace Theology by implication. However, that does not mean that the author of Ephesians did not later contradict that message (e.g. Ephesians 5:3-6), or that if one had asked the author later if he believed in Free Grace, that he would have agreed. He may have written something which has implications that he actually disagreed with, or rejected, because he was not careful, or did not fully think through what he was saying.
Additionally, the Gospel of John, from which come many of Free Grace's most important passages, is a blatant forgery. Until Free Grace Christians deal with this argument, and stop using John, they really cannot claim to be sincere followers of the person Jesus of Nazareth, who appears to have taught a rather straightforward works-based justification.
Free Grace Theology does make a kind of logical sense, and I do believe that it is the most logically sensible Soteriology, given the assumptions of the average Christian. However, unfortunately for them, their own text betrays them by making constructing a coherent, consistent Soteriology impossible, because it is the product of a false religious movement, centered around a preacher who repeatedly made false prophecies.
Finally, I still have a certain degree of respect for Free Grace Theology, because it is the only Soteriology which takes Ephesians 2:8-9 seriously, rather than turning it into meaningless, inconsequential doublespeak. Nearly all other Soteriologies favor the works-based passages over the "free gift" passages (John 4:10, Romans 5:15-18, 6:23, Ephesians 2:8-9), and therefore contain nonsense in their theological framework like a "free gift" which requires a lifetime of service, works done which are required to get to Heaven that nonetheless do not "merit" Salvation, and other similar theological clichés which make nonsense of language, and insult a thinking person's intelligence.