> The belief is that as sovereign nations, they can hold their own people accountable, and no one else should have the right to hold them accountable instead.

There is no such thing as a sovereign nation in the modern age.

Even if you ignore the dependence on international trade (i.e. relying on other nations to trade with you), sovereignty requires the military ability to defend yourself against any adversary trying to impose their will on you. In the nuclear age we've effectively abolished this concept thanks to Mutually Assured Destruction. If China wants the US gone, either China "wins" (i.e. the US surrenders or offers a compromise) or the world ends (i.e. the outcome of global thermonuclear war makes "US" and "China" meaningless concepts).

So if "as sovereign nations" is no more than a meaningful flourish, the belief becomes simply this:

> they can hold their own people accountable, and no on else should have the right to hold them accountable instead

We can break this down again:

> they can hold their own people accountable

It's interesting that you say "can", which already admits that there is a difference between the ability and willingness to do so. But even if we ignore this, the important consideration here is that there can be a mismatch between what "they" think "holding their own people accountable" means and what others think.

By "they" you reference the US and Israel but legal entities don't do anything, people do things. Granted, those people exist within social systems of power but at the end of the day people within those states will be the ones holding people accountable or not. If you think of this in terms of people, a potential conflict of interest becomes apparent: the people being held accountable are the military and political leadership and legislators, the people holding them accountable are military and political investigators and courts. The victims of the alleged crimes are not represented by either of these groups as Gazans are generally not fully Israeli citizens.

This isn't to say that Israel's legal system might be unfairly biased against Gazans or that it might err on the side of ignoring crimes against them or that this might be a systemic problem. My point is merely that there's a credible reason to believe that an investigation by Israel into alleged actions by its government against Gazans might be biased simply based on an in-group/out-group distinction between the involved groups.

> no one else should have the right to hold them accountable

This is begging the question of "accountable for what". You can only hold someone accountable if there's some bar they're supposed to meet. Israel was a signatory to the Rome Statute (although it walked back from it in 2002 along with the US) and we're talking about the ICC so the bar seems to be "upholding human rights and abstaining from human rights abuses and war crimes".

You might argue that no outside state should be allowed to intervene in another state's human rights abuses as long as they are contained to that state's territory or only people who are subjects of that state. But clearly Israel doesn't believe this or otherwise the Mossad wouldn't have a history of abductions and assassinations. And it's a good thing too because otherwise we wouldn't look at events like the Rwandan genocide as a horrific failure of the international community and instead just consider it business as usual.

Legally speaking, the ICC clearly has the "right to" do what it is doing. But if you mean morally, again I don't think you believe this unless you believe interventionism is never justified. In other words that would mean you want to go back to the Peace of Westphalia and abolish the notion of universal human rights entirely and allow states to commit genocides, engage in chattel slavery or do all kinds of unspeakable horrors as long as they do so within the confines of their own territory.

I don't think you're saying any of that. I think what you're instead arguing for is nothing more than special pleading: it's different when {the US, Israel} does it.