One that I've heard most is this event (actually two events) in which a man, accosted by lustful brutes in the dead of night, brutes that want to rape a male visitor/male visitors, who instead offers his virgin daughter/daughters/the visitor's wife. The argument is that this act is calloused and how can anyone considered religious believing and faithfully following a God of love be inclined to act so indecently as to offer his own daughters.
BUT: let's look at these events. The first one (in Genesis) is Lot. Lot is visited, shortly before the destruction of his famously sinful homeland of Sodom and Gomorrah, by two angellic figures. The two angels bore a message, as angels means messenger, of the destruction of the town and said they would spend the night in the village square. Lot, presumably knowing the kinds of things that go on at night (man-rape) insists they stay with him. Too late, apparently, the men of the town had already seen the figures and went ahead to accosting. Knowing these men were angels, Lot thought the worst thing that could happen was them getting manhandled so he offered his daughters. Compassionate to his daughters? maybe not, but it is shown later that he did love them, but acted in urgency and not under the instruction of God or the angels (who moments later blinded all the men so no tragedy would befall Lot, the angels, or his daughters). So, bad stuff happens in the square, lot protects angels, in an urgent time surrounded by a town full of men so vile that God destroyed them offers his daughters to keep them from raping angels. Seems more reasonable in that light, and God still protected the daughters rather than this tragedy befalling them.
The second case, Judges 19-21, a very parallel event happens in a time when "There was no king in Israel and everyone did what was right in his own eyes." A Levite man and his concubine are traveling through this city, another man sees them as they're about to crash in the village square and says "maybe you shouldn't stay out here" so he let's them into his house. Nasty man-villagers come a-callin but this time the people inside are not holy angels but a Levite who is not living up to the holy calling of his tribe. So what happens when the men ask the homeowner to rape his Levite guest? "Please, take my virgin daughter and his concubine" virgins were practically commodities in sinful times, it's unfortunate but not of God. This story definitely fits the "bad things happening" moniker, as the lawless Levite lets his lady out there then goes to bed while, well, bad things happen to her. It's not clear whether or not she's dead in the morning, but he treats her very coldly and when they get back to his home he cuts her up and sends her to the 12 tribes and says "look what the tribe of Benjamin did, this is awful." A war breaks out, the tribe of Benjamin is almost wiped out of extinction, more bad things happen.
At this point the atheist may be saying "this is why I don't believe in God," but when I read this story this morning I must admit I was shaken thinking "how did all this happen in the name of God?" But for Christians who may be thinking as I did, it is made clear by the last verse of the book of Judges, "
None of these events are condoned or warranted by the teachings of Jesus Christ, by the law, or by general human decency. These events happened as a result of idle hearts and idol worship (Judges 17-18), and the religious falling down on the job (the Levites were the priests).