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It is entirely possible that we do not understand the word "elect" the same way, but -- be it as it may -- could you explain then how is it that we have offended God willingly if we have no free will? And if we have offeneded God unwillingly, why is it an offense? Perhpas you can also explain how can God, Who is not subject to passion, be offended by unworthy scum (I believe that's close to how Calcinists see humanity)?

Sure,
Men have a free will that was bound by the sin of Adam. After the fall men still have a free will,but they will never choose "good" they will instead choose between the lesser of 2 evils, they will never choose to do "good " or be "good" ( as God calls good not men). So men have a "free" will that is in bondage to sin, men always serve their master, in this case the unsaved man has sin as his master.
I have heard it said by an evangelical Christian that before he was saved sin was never a "problem" to him, he just did it without a concern or guilt. That is the unregenerate, will at work.
Men will always choose according to his nature, an unregenerate mans nature will never desire to come to God .

That bondage must be broken by Gods grace before a man will have the ability to truly repent that sin and believe in Christ.

Paul expresses it like this

Rom 3:10 As it is written, There is none righteous, no, not one: 11 There is none that understandeth, there is none that seeketh after God. 12 They are all gone out of the way, they are together become unprofitable; there is none that doeth good, no, not one.

He notes the change with conversion

Eph 2:1 And you [hath he quickened], who were dead in trespasses and sins; 2 Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience::3 Among whom also we all had our conversation in times past in the lusts of our flesh, fulfilling the desires of the flesh and of the mind; and were by nature the children of wrath, even as others.

Rom 6:16 Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness? .Rom 6:20 For when ye were the servants of sin, ye were free from righteousness.21 What fruit had ye then in those things whereof ye are now ashamed? for the end of those things [is] death. 22 But now being made free from sin, and become servants to God, ye have your fruit unto holiness, and the end everlasting life.

So the unregenerate man can choose, but he will never chose Christ, he is a slave to his sin nature.