Capital markets are essential to a thriving economy. Without investors willing to fund new schools and factories, new businesses and non-governmental organizations, we'd have no innovation, no growth, no creation of wealth or jobs. As an economy becomes more dynamic, this steady infusion of investment becomes more important just to sustain normal growth and employment.
During a period of healthy growth, the equilibrium for capital markets and labor markets are coincident. Letting investment markets do their natural thing will result in new jobs and economic expansion.
The equilibrium for capital markets can shift. One day the price of capital can induce savers to invest and the next day it can convince them to hold their money in cash rather than make loans or fund new businesses.
This new equilibrium in capital markets shifts the equilibrium in labor markets. Unemployment can spike as capital sits idle.
This shift in equilibrium for capital and labor markets will drive down GDP. Sales will fall.
At this point, it's perfectly rational for every sector to sustain the recession. Households without jobs won't buy. Businesses without sales won't hire. Investors without sufficient number of employed households or expanding businesses to loan to will sit on their money.
In other words, at this point every "localized" market - labor, goods, and capital - will be in equilibrium. The good news is that the economy is stable. The bad news is that it has reached stability at recessionary levels. This general equilibrium needs to shift before it will make sense for investors, households, and businesses to change their behavior. There is nothing happening in the two other markets to drive a change in the third.
Government can make changes that will shift equilibrium in all the "localized" markets. By spending more, by cutting taxes, by putting more money into circulation or lowering interest rates, it can engineer temporary growth, helping to put an economy back on track for steady expansion. It can disrupt the equilibrium in the localized markets to get things moving again.
Valid rebuttals to Keynesian economics include criticism about a governments' ability to time stimulus, the level of downturn deserving of Keynesian stimulus, and the degree to which a Keynesian style intervention needs to be coordinated with other countries to be effective. You could even argue about whether expectations might mitigate the effect of such government policies.
Invalid rebuttals include "I don't like big government." Keynesian policy recommendations are incidental to the size of a government. Countries like Denmark (where government spending is 58% of GDP), Sweden (51%), Germany (45%) the US (41%), Mexico (27%), Singapore (17%), or the Philippines (16%) can all engage in Keynesian policies. Whether you want to emulate Southeast Asia or Northern Europe is irrelevant. Whether your long-term target for government spending is 50% of GDP or 15% of GDP, government spending can still be increased in the short-term in response to recessions and downturns. You can induce capital markets to engage in ways that stimulate the whole economy.
For me, the real genius of Keynes was his realization that reaching equilibrium in capital markets didn't automatically ensure equilibrium in the general economy. Before Keynes, we only had economics. After Keynes, we had microeconomics and macroeconomics. His policies were key to creating conditions that allowed the limit to shift from capital to knowledge workers.