Top 5 Lies About Israel’s Assault on Gaza , page 1

The reason lie #1 is a lie has nothing to do with anything given in response to it. It becomes a fallacy because you have structured three independent statements into one argument. Then you argue against a portion of what you have stated. The first statement is "Israel is only targeting legitimate military sites." The second is "(Israel) is seeking to protect innocent lives." The third is "Israel never targets civilians." As these are three separate, distinct arguments, let's analyze each one.

Israel is only targeting legitimate, military sites. At no point in your article do you provide any statement to the contrary. This statement is true, based on the information you have provided.

Israel is seeking to protect innocent lives. In Lie number five you state that Israel has notified civilians to flee from coming bombardment. Their notification has caused people not to be where an impending attack is while it happened. This statement is true based in part on what you have provided. It is also true because Israel has assisted in the evacuation of Palestinians that chose to leave for other countries.

Israel never targets civilians. The Israeli military selects military targets in Palestine. Hamas is both a political AND military group. The leaders are elected by the society they represent, as you pointed out. Although voluntary human shields are currently treated as civilians, international law does NOT preclude attacks on military targets with civilians present. "The presence of a protected person may not be used to render certain points or areas immune from military operations." Fourth Geneva Convention, Article 28

You make the same mistake in constructing lie #2. There are two statements here. First you state Hamas violated the cease-fire. They didn't. Neither did Israel. First I'll explain how Hamas didn't violate the cease fire. The two words we need to look at are hunda, and tahdiya. The difference between the two Arabic terms is substantial. Hudna means "truce," which is more concrete than tahdiya - "a period of calm" - which Hamas often uses to describe a simple cease-fire. In traditional Islamic thought, a hudna is negotiated between an Islamic entity and a non-Islamic entity, but it can be reversed the moment the Islamic side has gained sufficient strength to resume fighting. Nevertheless, a hudna implies recognition of the other party's actual existence, without acknowledging its legitimacy.
A tahdiya has less standing than a hudna. Khaled Mashaal, Hamas' leader, and his deputy in leadership, Musa Abu Marzouq, elaborated in recent months their interpretation of a tahdiya. In an interview with Al-Jazeera (April 26, 2008), Mashaal clarified that for Hamas, a tahdiya is "a tactic in conflict management and a phase in the framework of the resistance [meaning all forms of struggle]." He added that it "is not unusual for the resistance…to escalate sometimes and to retreat a bit sometimes as the tide does….The tahdiya creates a formulation that will force Israel…to remove the siege…and if it happens it will be a remarkable achievement….We are speaking of a tactical tahdiya….As long as there is occupation, there is no other way but resistance."
Now I'll explain how Israel didn't violate the cease-fire. On December 18th a six month ceasefire between Israel and Palestinian militants in Gaza expired. Late on that Thursday Hamas announced it would not be extending the truce. The Hamas spokesman, Fawzi Barhoum, says the Palestinian people don't feel they have anything to gain by keeping the ceasefire in place.
The Israeli bombardment is a response to Palestinian rocket fire and is designed to end such rocket attacks. The rocket attacks from Palestine are public record, and are mentioned in your own article. Israel did respond to the rocket attacks. There is no fallacy here.