How to replace this washing machine valve/faucet?
The threaded part on the valve where the hose connects seems, from the picture, to be rather short. It is possible that the part on the end of the hose is interfering with the valve body (represented by the green arrows in the diagram below) before the rubber hose washer gets a decent amount of compression on it.

If this is the case you may be able to purchase a thicker hose washer that is more supple than what is currently in the hose end to allow for the proper compression to seal the joint.
Also, as stated previously in the comments, it is often necessary to use a tool to turn the hose coupling tight to get a good seal.