One of the chief theological opponents of John Owen was Socinianism. Carl Trueman explains:

Socinianism takes it name from an uncle and a nephew, Laelius and Faustus Socinus, a couple of Italians, who in the 16th century decided to push the Reformation as they saw it to its logical conclusion. Remember what I said about the Reformers, they had a critical attitude towards the church’s tradition, but one that was appreciatative. The Socini would have none of that. The Socini were pretty much a “no creed but the Bible” sort of people.” As far as the Socinians were concerned, the church had gone wrong almost as soon as the canon was closed, and it went wrong because it allowed Greek philosophical language to intrude. The Socinians wanted to get rid of all philosophical language in Christian theology. They wanted to just go back to the bare texts of Scripture. The result was a theology that was (surprise, surprise) Unitarian. Guess what? If you get rid of all the Greek philosophical vocabulary in Christian theology, you cannot express God’s threeness-in-oneness in anything approximating a coherent way. You simply can’t do it. And historically it’s the case that whenever people have tried to purge Christianity of what we would call metaphysical language, philosophical language, it always ends up in Unitarianism.

Socinianism was not only Unitarian, but (obviously) denied the deity of Christ, the eternal damnation of the wicked, and the substitutionary atonement of Christ, among other things. And all this was done in an appeal to the “express words of Scripture.” Later Trueman summarizes part of Owen’s dilemma.

Socinianism . . . is particularly dangerous, of course, because it says it’s just following the sayings of Scripture. It’s a “Scripture alone” movement, which is principally what Owen wants to say he is.

Owen addressed this “scripture only” claim at the beginning of his Vindiciae Evangelicae:

MR BIDDLE having imposed upon himself the task of insinuating his abominations by applying the express words of Scripture in way of answer to his captious and sophistical queries, was much straitened in the very entrance, in that he could not find any text or tittle in them that is capable of being wrested to give the least color to those imperfections which the residue of men with whom he is, in the whole system of his doctrine, in compliance and communion, do charge them withal: as, that there are contradictions in them, though in things of less importance; that many things are or may be changed and altered in them; that some of the books of the Old Testament are lost; and that those that remain are not of any necessity to Christians, although they may be read with profit. Their subjecting them, also, and all their assertions, to the last judgment of reason, is of the same nature with the other. But it not being my purpose to pursue his opinions through all the secret windings and turnings of them, so [as] to drive them to their proper issue, but only to discover the sophistry and falseness of those insinuations which grossly and palpably overthrow the foundations of Christianity, I shall not force him to speak to any thing beyond what he hath expressly delivered himself unto.

In other words, Owen agrees that his theology does not go beyond what the Scripture says, and can show that Socinianism is not in accordance with the Scriptures, despite their so-called adherence to the “express words of Scripture.” In the end, such an appeal is really a means of denying the teachings of Scriptures. Trueman concludes,

I have a sneaking suspicion that a lot of contemporary Protestantism is functionally Socinian. Not only is it Unitarian, but also it pays no attention to what the Church has said over the centuries; it does not listen to it to see if there is any wisdom to be gleaned there from.