Hello, there was an answer that we can cast Squee under Binding. However…
601.2 says

A player must be legally allowed to cast the spell to begin this process (see rule 601.3), ignoring any effect that would prohibit that spell from being cast based on information determined during that spell’s proposal.

I thought we cannot even begin casting process because casting Squee is prohibited. (and it is not based on information determined during casting process)

Do I misunderstand this rule?

Magic's rules are permissive in nature–everything is forbidden by default, and you can only do things that the cards or rules tell you you can do. When 601.2 says that you must be legally allowed to cast the spell to begin the casting process, it's saying that there must exist a rule or effect that could permit you to cast that card in the first place–you can't, for example, propose casting every card from your opponent's hand so that they get put onto the stack and you can see what they are. No matter whether you will ultimately end up being able to cast that card or not, in order for you to even begin the proposal, there must be some rule or effect saying “you are allowed to do this”.

Effects that could potentially prohibit the casting of the spell–that say "you are not allowed to do this"–are different. Those are checked later, in 601.2e, including the effect from Ixalan's Binding.