“Does God exist” or “Christians are hypocrites”...
These are not foolish questions but very truthful statements and before these stumbling blocks are removed, they won't be able to receive the Gospel.
If you use the word "argument" in the sense of irrational arguments, I agree. These don't do any good. But you should clarify what you mean. Argument in general encompasses both rational and irrational arguments. Whenever you present the gospel to someone and they disagree , that is an argument started right there.
Rational arguments are as you said, reasonings, exhortation, etc, that attempts to convince a person through well-thought out logical arguments with supporting evidence (Scripture, history, experience etc).
Nothing wrong with these.
In evangelism, these kind of arguments are unavoidable and Christians have many apologetics resources available today to be able to dispute.
There's nothing wrong with arguments that make unbelievers angry.
That is why the opponents of the Christian most often wanted to kill them!
Examples:
Barnabus:
Act 9:29 And he spake boldly in the name of the Lord Jesus, and disputed against the Grecians: but they went about to slay him.
Paul:
Act 17:16 Now while Paul waited for them at Athens, his spirit was stirred in him, when he saw the city wholly given to idolatry.
Act 17:17 Therefore disputed he in the synagogue with the Jews, and with the devout persons, and in the market daily with them that met with him.
You know why there's not many converts today don't you?
Because people use methods such as you described, which is going to unbelievers with a feather and tickling them with niceties rather than sticking a sword (of God's Word) right into their heart and mind.
The way we love people is to declare the Gospel, don't confuse God's type of love with the love of this world, pluralism, relativism, new age, humanism, which is basically elevating man above God , and have more respect for the feelings of the unbeliever than actually doing what God commands by preaching the truth, even if it hurts. But watch out, the tolerance and politically correct police are out in force! Even in the church.