That is the Arminian rally cry, and the antithesis of the 'U' in TULIP, right?
Wrong. The statement I chose God from my own free will! is a far better fit for Calvinism that Arminianism.
In Arminianism, the sinner is wooed by God. He knocks on the sinner's door. He patiently seeks the sinner and provides him the opportunity to accept or reject the gospel. (Leaving aside those multitudes who never hear the gospel. How unfair!) God cradles the head of the wretched, dying sinner in his lap. He gently places the elixir of life in the sinner's mouth. The sinner merely decides whether to swallow the divine medicine. If he does, then he is regenerated. The teeny amount of free will used by the believer is merely a rational assent by a person after a prolonged one-sided courtship; a courtship is which the pursuer (God) sometimes fails. Only after (if he is lucky) realizing that there is no better alternative, does the sinner "give in" and accept the gospel.
His free will does not tell him to seek God wholeheartedly before regeneration. Arminianism acknowledges that grace, acting against the inclinations of the will, is required, and that unregenerate man does not choose, unilaterally, to seek sufficiently after the true God. No, grace, which I earlier called "wooing", is needed. But man is not totally depraved, and a small vestigial goodness is present which allows his free will to accept the gospel, but only after God has worked on him and brought him to the point where the choice should be obvious. The remnant goodness allows anyone (if they get to hear the gospel) to be saved, but Arminianism cannot explain why some sinners choose yes while others choose no. Did one have microscopically more after-the-fall left-over goodness? Was God's grace slightly inadequate in the case of the sinner who declined the gospel? Who knows.
In Calvinism, on the other hand, the sinner uses his free will completely, throughout the process. The same will he is born with, the same one he will have in heaven, is used to choose God. The difference, of course, is that Calvinism teaches total, not just nearly-total depravity. The unregenerate sinner will never choose God. So God regenerates sinners without requiring an assent, an assent of which they are morally incapable. After being regenerated, the sinner chooses God wholeheartedly, with total conviction of his free will. He makes a big, free, and willing choice, not a small coerced one.