Consider a common scenario where you SELECT a set of rows and take a SUM over a column. Suppose your query and another query begin reading from the same committed state of the same table. Suppose that the other query uses an UPDATE command on a set of rows in the table, and that the other query commits before yours does. In order to be consistent, the database system must detect the situation where the other query updated a row that affects the filter WHERE you scanned the table, otherwise your sum could be incorrect if the other query's committed state would cause your query to compute a SUM over a different set of rows or over modified values in your SUM. The only way for the database system to guarantee there is no conflict is to keep track of every single row your query accesses, even if it is a row passed over by a WHERE clause!
Serializability is a well studied concept. You can find lots of good resources about algorithms for implementing concurrency control and for detecting whether or not two transactions are serializable. The high-level summary is that it takes a lot of operational bookkeeping to guarantee that two queries have no conflicts, especially when you are using real-world examples having many filters and joins.