Difficulty in finding protein inhibition drugs
Drug production is very long, tedious and costly process. It generally takes more than 10 years to make entirely new drug. It has various iterative aspects. take a look at following cartoon showing various steps in drug design ( Taken from Anderson 2003 )



Now coming to your questions, 


  what is the difficulty in producing drugs that inhibit production by a certain protein?


First of all you need to know other effects of that protein which might be essential for normal cell function. For example, there are many genes overexpression patterns which have correlated with cancer. This suggest excess quantity of these proteins/factors leads to cancer. Now one would like to block these proteins with inhibitors. However if you block these proteins, they might also affect regular cellular function. For example, SHC1 overexpression is correlated with breast cancer. However that protein is very important in apoptosis regulation, EGFR pathway, Oxidative stress and many more functions. Now if you inhibit this protein, your normal cells will also get damaged. 


  Isn't it about analyzing the chemical makeup and structure of the protein and finding ways to neutralize it


It is not that simple, for this you need inhibitor which can specifically either bind (it can be competition also) specifically with given protein. Most of the time there are other problems like , there might be other proteins with that structure which can affect other protein's function. There will be other important problems like


Delivery of inhibitor
Specificity (Inhibitor need to act only on target cells)
Sensitivity (Inhibitor need to be sensitive enough to get full response in low concentration)
Side effects (There might be side effects of this inhibitor which should be minimized)
Cell resistance (Many times cell becomes resistant to inhibitor) 


Above mentioned points are actually major issues in all cancer treatments like Chemotherapy  , Radiation therapy, Immunotherapy , Hormone therapy etc.