The correct answer is A. for.
The word “responsible” means “being accountable for something”. In this case, the person is accountable to the president for his decisions. This means that the president has the authority to hold the person accountable for his decisions, and to take action if the person does not make good decisions.
The other options are not correct because they do not convey the meaning of accountability. The word “of” means “belonging to” or “associated with”. The word “to” means “in order to” or “directed towards”. The word “with” means “together with” or “in the company of”.
In this case, the person is not simply associated with the president, or directed towards the president, or in the company of the president. The person is accountable to the president, which means that the president has the authority to hold the person accountable for his decisions.