Here's a devils advocate type answer. On balance, I err on the side of Israel rather than Hamas but am not a die hard supporter. I say that because comments below may appear to make me out as such, but I'm just trying to represent the coherent argument for the sake of discussion rather than the strength of my own views per se. For the record I regard the suffering of innocent people in Gaza as grotesque.
Settlements.
The justification for this behaviour is complicated but essentially amounts to the belief that the Geneva conventions were not drafted with Israel's particular dilemma in mind. The Geneva conventions were drafted by European powers for whom the annexing of territory was strategic and imperially motivated rather than existential. Israel does not believe it can have security if a Palestinian state is established in the West Bank. The justification for this being Arab/Egyptian aggression in '48, '56, '63, and '73. Not to mention more recent state sponsored actions by Hezbollah, Hamas et al. A Palestinian state on the West Bank could maintain a standing army on the Israeli border, could invite other Arab nations' armies to base themselves there. Echos of the previous conflicts listed above. This is unconscionable for Israel, one only needs to glance at the map to see how indefensible its position is if a foreign army was amassed on the West Bank. Ignoring settler activity or evicting Palestinians if a single member of their family commits any kind of act against Israel is just a convenient way to achieve the larger goal. The settlers of course are a lot more religiously / ethnically motivated. The government is too but I think realpolitik plays a larger role.
Gaza civilians
The capricious and deliberate targeting of civilians and children with no other goal is of course horrific. Israel of course will maintain that that's not what they're doing, that they are acting on intelligence against Hamas who are using people as human shields. Which is also horrific but is a different type of justification. Everyone of course will have decided in their own minds if they believe what Israel says about its intelligence or whether they believe what Hamas says about their lack of presence in an area.
If we assume for a moment that Israel is being honest about that particular aspect: that they are ok killing innocent people and children if Hamas die too. What's the justification for that? I think their view is that they're dealing with a problem that no Western country has to deal with. Britain has seen maybe a hundred deaths over 25 years from about 20 Islamic extremists. The US has seen 3000+ deaths from a similar number. In both cases the number of Islamic extremists are small enough that you could remember their individual names. Israel on the other hand has ~25,000 signed up members of Al Qassam terror brigades on their doorstep. That is a different level of threat all together, by three orders of magnitude. Hamas will not engage with the Israeli military in a standing battle because they would lose. So they are engaging in a guerrilla type strategy where shielding themselves behind civilians is an integral part so they can opportunistically strike out in suicidal attacks. It doesn't happen accidentally, but repeatedly, it's a core part of their strategy. A state needs to decide whether they're ok with Al Qassam brigades existing or killing the civilians they surround themselves with. It's a shitty choice, but it is a choice Israel sees as Hamas' when they choose their mode of fighting. Leaving Hamas free to plot their next maraudering attack on Israeli civilians is unconscionable, so the death of Hamas human shields has to be ok. There isn't another way.
This is a situation so unfamiliar to the West that it is easy to see it as capricious and brutal, horrific and evil. And the death of innocent people are those things, but one has to see the trolley dilemma in full.
America actually has been in this type of situation, only once as far as I'm aware, and it provides a useful insight into how Western countries justify themselves when confronted with the same dilemma. On 9/11, United 93 was identified as under terrorist control and inbound to Washington DC. Fighter jets were dispatched to shoot it down. The deaths of the 40 innocent people on board would obviously be horrific, but one can see the logic that letting a terrorist controlled plane be flown into a densely populated city would be to cause the deaths of hundreds of even thousands.
Was the mission to shoot down United 93 the right one? Was it evil? What if those 40 civilians had been 40 orphans on their way to be placed with foster families? How completely horrific does the situation have to be before it's better to let the terrorists fly they plane into hundreds or thousands of people?
Israel sees itself caught in this kind of dilemma 24/7 with Hamas. Each signed up member has the proven intention to cross the border and maraude around killing grandparents, babies, children. So Israel calculates that, regrettably, it is necessary to kill them and the civilian shield they themselves have created. It is a shitty awful dilemma with evil on both sides, but Israel feels justified holding Hamas to blame for their human shields deaths the same way most of the American public would have blamed Al-Qaeda if the US Air force had managed to shoot down United 93. (The fact that in reality events meant they didn't have to doesn't take away from the logic of what they were prepared to do)
