For Wesley and other Arminians, original sin is not a matter of predestination but of human nature.
In his sermon Original Sin, Wesley states:
The Scripture avers, that "by one man's disobedience all men were constituted sinners;" that "in Adam all died," spiritually died, lost the life and the image of God; that fallen, sinful Adam then "begat a son in his own likeness;" -- nor was it possible he should beget him in any other; for "who can bring a clean thing out of an unclean?" -- that consequently we, as well as other men, were by nature "dead in trespasses and sins," "without hope, without God in the world," and therefore "children of wrath;" that every man may say, "I was shapen in wickedness, and in sin did my mother conceive me;" that "there is no difference," in that "all have sinned and come short of the glory of God," of that glorious image of God wherein man was originally created.
According to Wesley, our free will (which he calls "self-will") is inherently sinful. We have a choice of following God's will or our own. When we choose to exercise our own will, we turn our back on the will of God.
Satan has stamped his own image on our heart in self-will also. "I will," said he, before he was cast out of heaven, "I will sit upon the sides of the north;" I will do my own will and pleasure, independently on that of my Creator. The same does every man born into the world say, and that in a thousand instances; nay, and avow it too, without ever blushing upon the account, without either fear or shame. Ask the man, "Why did you do this?" He answers, "Because I had a mind to it." What is this but, "Because it was my will;" that is, in effect, because the devil and I agreed; because Satan and I govern our actions by one and the same principle. The will of God, mean time, is not in his thoughts, is not considered in the least degree.