What are the most difficult situation regarding objections from customers?

I think so B. Accepting the faults is very tough task.

I consider objections are a part of sales and it does not put me in difficultly at all. In fact it gives me a better change to explain my product or service to the customer. As there are options given i will go with

B. When the objection of the customer is exactly what you feel about your own product

D. When the objections are about the product and quality 

when they express doubts about product quality, the training of your personnel, speed or responsiveness of service, or compatibility.

option D

Option (B)   >>>>>  When the objection of the customer is exactly what you feel about your own product.

It is very difficult to explain things other than what you have in your mind. Someday or other you will come with a contradictory opinion about the same thing and may cut a sorry figure.

I am going to go with B & D, ...if I have the same objection than the customer it is over the quality of the product and not performing to standard.  In this case I would give the customer the full value of the purchasing price back and command a better product, even if it is not ours;

My boss may not like it, however it will initiate a recall or change in design to get a great product ... the customer will remember and purchase from you again, since he knows that you are honest. 

D. When the objections are about the product and quality

B. When the objection of the customer is exactly what you feel about your own product

I think other Objection's could be tackled, issues happen to be resolved. But, if we also have any objections too & if customer also raises the same objection, I think that is the 'Moment of truth'. It would be real difficult situation for an 'Ethical Negotiator' ... :-)

WHEN THE OBJECTIONS ARE ABOUT THE PRICE

B. when the objection of the customer is exactly what you feel about your own product

In general, any objection could be noted as a " negative point" toward the product or the service that  a company provides because customer feels bad towards his satisfaction regardless if it is the price or the quality, because customers always follow the rule of " customer is always right" !!!

Therefore I would say that all the objections that you mentioned could hurt the company, but it you want to point the most critical one, it could be "D" since the quality and the product are what the customer look for.