:1)What arguments you do not find convincing?  

 :2) Almost all sources describe this as "Gaza Strip airstrikes" or  "Gaza Strip air strikes". If I understand your point, you are saying that ''Operation Cast Lead is a convention, and that it stems from sources. This is valid point, however, it fails to convince: 

 :a)it isn't a convention to name articles by operation names, it is a consensus among a set of editors, and WP:CCC and it cannot happen outside of neutrality. If it is a convention, please name the policy or guideline establishing it so we can learn it. 

 :b) it is not neutral as it is the name that one side is giving to the conflict. This is frank truism, like 2+2=4. If you name something, you have the upper hand in framing it. Hence no neutrality. This like saying the sky is blue or that the Holocaust happened. I first came upon this name as operation thing in 2006 Lebanon War, and then in was agreed not to use it. But I am not oppose to its use, I am opposed to its use when it obviously breaks neutrality. That's the difference. 

 :c)None of the non-partisan reliable sources are calling this Operation Cast Lead''', they are saying what we are saying in the lead: That the IDF is calling it Operation Cast Lead. Yet we have highly reliable sources calling this "Gaza Air Strike" with no mention of Operation Cast Lead Time Magazine, Fox News, Associated Press, etc etc etc. And then even inside of Israel, the sources don't use the term Haaretz. I do not know what sources you are reading, but we are reading different ones. And I am reading all the usual suspects for an event like this. (Yeah, Haaretz has useed "Operation Cast Lead", but also has written about this *without* the operation name; if Haaretz can be neutral, why can't wikipedia? 

 :3) AFAIK, in all of the "current event" articles I have worked in, including recently the November 2008 Mumbai attacks (which I proposed its structure, and are its third highest editor) use the "date, place, event - format" which is an informal convention used in conflict articles (for relevant cases see above Lebanon War examples). The only naming convention that specifies a format is the WikiProject Disaster's convention, which uses the "date, place, event format". This is an emerging, informal convention, with which I agree. Now, as to the naming of Israeli operations,  

 :4)The date specificity is a disambiguation requirement due to limitations with the Wikipedia software, and shouldn't be a subject of debate, please see WP:NAME.  

 I have provided you with sources, and with evidence to my assertions. I believe it would serve us well if we minimize naked assertions, and concentrate on providing evidence. I am very open to convincing, but we'll need more than just our word, we need sources. Thanks!