Then your view of responsibility is flawed, IMO. If someone is 'responsible' then they are 'response able' (able to respond).
Calvinism removes that ability thus cannot consistently maintain any real since of 'responsibility' without completely redefining the word itself.
Even the heathen wouldn't beat a dog for not coming when called if they themselves chained the dog to a pole. According to Calvinism, God chained all men from birth to their depravity as a punishment for Adam's sin, but then he makes an appeal for all of them to come to him and be reconciled...then He punishes those who do not come. Any objective observer would find this view completely disingenuous and unjust. I know, I know, we all deserve hell, but we agree on that point. We are talking about God appeal for all to be reconciled to Him so they can avoid destruction. We are talking about his calling the dog who HE chained to the pole and then punishing that dog for not coming.
With all due respect, you are missing the connection between 'ability' and 'will'. In the scenario of the dog chained to a pole, you are neglecting the dog's will. He loves his chain, and he loves his pole. He does not seek to be released. That is why the dog's nature, his will, MUST be changed first.
Consider the sinfulness of mankind. We are slaves to sin, and rebels against God. Does a rebel desire to be reunited with his King? When I discuss theology with my atheist friends, they always tell me that they are at peace with themselves, do not feel any emptiness, and have no need for God. Does this look like a slave chained to a pole just begging to be released? No. Those who are slaves to sin are WILLING slaves. They LOVE their sin and their rebellion. They do not even think they have chains. They actually think of themselves as FREE. Freedom from God can only mean slavery to sin, but they don't believe that. Nothing inside themselves is going to motivate them to stop loving their sin. Only by spiritual surgery does God grant them a NEW NATURE, which sets their will free from sin.
That is the problem with the arguments for autonomous free will. I also find it very interesting that some people argue for man's free will to respond to God (naturally, without God's saving grace), but they also believe that a person cannot lose their salvation. That is a predicament you see, because on the one hand they say that man is free to accept or reject the gospel on his own, but once he has accepted it he actually loses freedom in the hands of God and can no longer reject Christ and lose his salvation. So apparently God 'respects' the free-will of man prior to man coming to faith in Christ, but then God 'no longer respects' the free-will of man once he is in Christ.
Those who have held to Calvinism have ALWAYS made it clear that God is sovereign and man is responsible. Those who attack Calvinism try to paint a picture of a sinner who is unable to obey God, but is trying really hard to do so (the chained dog who wants to be set free). Yet the fact is that the unbeliever is unable to obey God BECAUSE HE IS UNWILLING. We cannot talk about the ability to do something without reference to the will to do it. I mean, when I say that "I am able to drive a car" the implication is that IF I WERE WILLING to do it, I could. But my action of driving the car, even if I were physically able to do so, is totally and completely dependent upon my will to do so. So long as I remain unwilling to drive a car, I will never drive it.
THAT is the state of the sinner. The sinner is UNWILLING to stop rebelling against God. The unbeliever is UNWILLING to bend the knee to Christ. Some other external force (God's action) is required in order to CHANGE the person's heart. That is why those who deny total depravity argue for autonomous free will. The human will MUST be able to change itself at a moment's notice, without cause, without influence. Man must be completely autonomous, which means that his actions are NEVER caused by anything. In all honestly this puts man on equal footing with God. God's will is not caused by external influences. God is the uncaused first cause. But at the same time, if we hold to autonomous free will in man, we are saying that man IS JUST AS FREE AS GOD, JUST AS AUTONMOUS, and JUST AS FREE FROM INFLUENCE. Man's will becomes uncaused. That is why the belief in human autonomous free will is completely unbiblical, because it sets man as equally free as God.
In the end, let me summarize with a scenario. Let's say that 100 atheists go to church and hear THE EXACT SAME SERMON. Let's say that only 10 of them accept Christ. Why didn't the other 90 accept Christ? They heard the same words, from the same preacher. How comes those words were effective on 10 people but not effective on the other 90? I will submit to you that there are only two possible answers to this question. Either there is something inherently different about those 10 people that allowed them to respond to the gospel, or it was God who chose in that moment to do open heart surgery on those 10 individuals, effectually calling them to himself. Consider that all 100 people heard the same general call of the gospel, but for SOME REASON, only 10 accepted Christ. The REASON for this is either found in man, or in God. Either those 10 people were somehow naturally different from the other 90 (they were more spiritual, smarter, better educated, better upbringing), or God supernaturally did something to those 10 people that he didn't do to the other 90. I think if you truly ponder this scenario, you will see that those who deny God's sovereignty (and FREEDOM) in salvation end up placing salvation somewhere else (namely in the hands of men).