I must correct some of the previous answers.
много is an adverb only when used with verbs. For example "много работать" - to work much.
When много is used with a noun it is a cardinal numeral (at list my vocabulary says so) and follows the rule that cardinal numerals (with some exceptions) require genitive after them.
As for intuitive reason... just get used to the language and you will find the reason. It works only that way. As well as in English.![]()