I won't get to Israeli motivations/statements much as that's been touched on in other answers aplenty, but an additional issue, as explained by the US is that Israel wants to inspect every truck--in Israel. So trucks that make it to Rafah have first to go to Israel then back to Egypt. E.g.
ADMINISTRATOR POWER: During the humanitarian pause, we established a new normal in terms of the flow of trucks into Gaza, getting up to around 250 trucks, getting up to 120,000 liters of fuel. Again, that should be the baseline going forward. There are many things that now are preventing us from reaching those numbers. Partly, it is because we need the inspections to move more quickly, and we need more inspection capacity. We understand very much why Israel wants to inspect what is going into Gaza after what happened on October 7. I think any country would wish to know what was going in, but that process absolutely can be accelerated. And opening Kerem Shalom to inspection – we heard from the UN, and from the Egyptian Red Crescent – would be very, very helpful.
According to Egypt and the US, this roundabout process
was the bottleneck, at least at one point, mid-November.
Miller: [...] The question is about screening mechanisms and being able to screen the number of trucks. There’s plenty of room for Rafah to get enough trucks through to deliver humanitarian assistance. The question has been getting those trucks screened, getting a significant – an appropriate number of trucks screened and in through Rafah. [...]
QUESTION: Does that mean Israel is dragging its feet or slow-walking those inspections?
MR MILLER: It means we have had – we have had difficulty reaching an agreement on the appropriate inspection mechanism. I’ll leave it at that.
Aslo, Israel doesn't want to let much fuel in, so it would not be diverted by Hamas. And, so that has had a ripple on effect on distributing aid inside Gaza, according to the US State Department mid-Nov:
Miller: [...] the implementers had run out of fuel to do that aid, and so we got fuel in yesterday to allow those delivery trucks to continue to do their work. But because – because the warehouses were full, no trucks moved in yesterday because they didn’t – they didn’t have anywhere to unload.
IDF-released footage shows that some Hamas tunnels have electrically powered ventilation and communication systems, even with air-conditioning units in some larger spaces. So not allowing fuel for generators to power that seems part of the reason.
And it's hard to find very explicit statements on this by officials, but my impression is that at least some of the extra aid was essentially conditioned on the release of hostages, at least in the way the ceasefire terms were arranged, or at least Hamas and some of the Western press understood them that way;
Aid trucks have begun to enter the Gaza Strip as part of the cease-fire and hostage release deal between Israel and Hamas.
Hamas on Saturday delayed the second group of hostage releases under a four-day truce agreement amid a dispute with Israel over the amount of aid entering the Gaza Strip, according to media reports.
N.B., there was one US official (McGurk) who said something that can be interpreted like that, but... read it carefully... he claims Hamas wanted that kind of bargain:
Now, such a release of large number of hostages would result in a significant pause in fighting, a significant pause in fighting, and a massive surge of humanitarian relief — hundreds and hundreds of trucks on a sustained basis entering Gaza from Egypt.
And I have to say, Hamas from the earliest days has said, if you want the hostages returned, we need fuel, humanitarian, more humanitarian supplies. That’s the bargain they set.