Individual stock prices go up because more people want to buy at the existing price level than want to sell, and they go down because of the opposite. The market in general goes up and down because of the collective actions of the individual stocks.
To some exent, saying anything more than this is speculation and BS. However, to give business reporters some credit, they are answering the question of why there are more people interested in buying or selling either individual stocks, groups of stocks, or the market as a whole. Typically, they can get to this by asking the question of what changed immediately before the price movement happened.
If a particular company announces its earnings, and then its price immediately falls, it’s probably fair to say that the stock fell on the news of the earnings release. If other companies in the same industry fell simultaneously, it is probably fair to say something like: “Auto stocks fell on the news of GM’s disappointing earnings.” Now, some of that is accurate, and some of it relates to other things: “Auto stocks also fell because Bob Smith sold the dozen shares of Ford he inherited from his late grandmother.” However, when there is a major news item and logically related move in stock prices, reporters will often, and largely accurately, report that the one “caused” the other, recognizing that there are numerous other factors in there.
When there is an unexpected news release, the market will react after the news. However, when there is an expectation of something economically relevant happening, traders will buy or sell in anticipation of the expected thing happening to “get a jump” on it. Something widely anticipated like the half-point rate cut at the Fed’s scheduled meeting today will be almost entirely processed by the market before it happens. As a result, once the anticipated happened, there wasn’t much market movement. However, if something unanticipated happened (like a quarter point or three-quarters point cut), there would have been intense trading and market movement.
Often business reporters will talk with people actually trading, either on the floor of the exchanges or in the major trading firms, who will explain why they are buying or selling, so they can get some idea of part of the reason the market is going one way or the other.
Is it pretty speculative why the market moves, yes. Are the reporters ever able to get behind all of the reasons for the moves, of course not. Are they sometimes essentialy bullshitting, sure. But is the information frequently useful to understanding the broad outlines of market movements, yes.