The verb "motivate" derives from the noun "motive." A "motive" is a reason or cause for an action. "To motivate" means to encourage, instill, or provide that motive.
Since inanimate objects and concepts cannot think on their own or have reasons for action, such objects/concepts do not have motives and cannot be motivated.
So your friend is right. The object of the verb "motivate" should be a being that has the ability to take action for a reason -- a being that can have a "motive." This would typically be a person, but it could also be an animal.
With your example of job interview question ("Why should we hire you?"), it would not be appropriate to ask the candidate to "motivate the answer" because an answer has no will and cannot take action. But it would be appropriate to ask the candidate to motivate the interviewer to take an action. For example:
- "Provide an answer that will motivate me to hire you," or just
- "Motivate me to hire you."
The object being motivated is the interviewer. The candidate will provide a reason or motive (the answer to the question) for the interviewer to take action (hire the candidate).
A couple of additional notes:
The noun "motivation" -- which derives from the verb "motivate" and describes the state of being motivated -- is roughly synonymous with the noun "motive."
The word "motive" can also be used as an adjective, and, in that usage, it indicates the production of motion. For example: "Combustion provides the motive power to move the pistons in a combusion engine." You can see that the noun and the adjective are conceptually related. A "motive" (noun) moves a person to action, while a "motive force" (adjective) indicates a force that moves physical objects.