When you get people supporting sides in a dispute there are always differences in the level of support given.
There are those who generally advocate support for one side but are able to see when one side is behaving unethically and beyond any sense of human decency.
Israel's action at Qana is inexcusable. I say this as someone who supports Israel's right to defend itself against those who attack it, those who send missiles against its civilians and who intend its destruction as a state.That's an example of good advocacy that supports one side of an issue but is never too biased to see ethical failings on that side.
Then you get those who know which side of the issue they are on and anything which threatens their blinkered little world view - "I am always right" - gets theorised away as some conspiracy. There's a link at those oh, so nice guys at LGF which constructs a conspiracy theory abut the timing of the collapse of the building at Qana, pointing to Hezbollah as the source of the demolition and a morgue at Tyre as the source of the bodies. Such are the excuses put up to argue "my side is always on the side of the angels". (You'll notice there are no links to this conspiratorial claptrap but if you are interested there's enough clues to google.) And, for those who aren't paying attention, I consider that an example of morally bad advocacy.
I'm sure you could find equally unbiased and biased postings by those who support Hezbollah but I don't want to spend all my time looking at the ravings of those who support, at the level of "national liberation army" or "resistance movement" (it's part of the government so what is it resisting in Lebanon?) or at the level of anti-Semitic rantings like "smash the Jewish state".
For the record, my own position is that Israel has a right to defend itself but when it kills innocents (non-combatants, or call them what you like I don't think the terminology is important) it loses much of the ethical and moral and sheer rightful backing it needs, and deserves.
For discussion on media portrayals of the events at Qana see this news roundup from the Washington Post.