When spraying water, why does the end of the garden hose have a force opposite to the direction of the water flow?

If your hose was absolutely perfectly straight, this would be true. However, hoses typically have bends in them. If we look at any given bend (such as the last one in a hose), we find that there is a transfer of momentum from the water to the hose to make up for the fact that the water entering that part of the hose is in a different direction from how it exits. This causes that section of tubing to move, bending another section, causing it to impart momentum to the tube.

We also never see a perfectly straight hose because it is unstable. If you had one, there would be force applied on the entire tube from the outflow of water, ending at the faucet. This causes the tube to bend in one direction or another, and from then on the, previously described effects occur.