Because it's a word that only (usually) exists in the singular form, like the words 'information' or 'advice' : nouns that are always singular. Remember that the idea of mass and unit is a grammatical distinction, not a 'real world' one. There's no point in scratching your head about really counting money, or wondering why we can't count 'rice' but we can count 'noodles'. It's not about the real objects at all - it's just about whether the word has a plural form or not. If there is no plural form ( in this sense of the word), then it's uncountable. It really is that simple.

It's not because the amount is infinite. Some nouns are uncountable because they are a 'mass' or a 'whole.' Examples: milk, rice, snow, advice, luck, luggage. I'm speaking about American English here. If I I remember correctly, British English treats these nouns slightly different than does AmE. I'm not an expert on BrE though.

Hello, Maia. It seems that you're a little bit confused with the fact that you can count the amount of money. If I can count it, how it can be uncountable? It is going to be useful to you understand what is an abstraction. So, an abstraction is a concept that acts as a super-categorical noun for all subordinate concepts and connects any related concepts as a group, field, or category. Got it? You should realize that the word money is an abstraction, it is a metaphorical way to refer to currency independent of the amount. As properly answered the dear Jerry before, as a whole. You cannot say "moneys". It doesn't make sense because it is already a general way to talk about currency, it is no specific.

Because there's an infinite amount of numbers existing.