After years of working with clients and bosses I have learned to always ask, "Why?". For instance in your situation I would be asking, "What's the problem you are trying to solve with using a photograph?".
This does two things:
- It reframes the question from design specifics to a language you both speak well
- It reframes allows your boss to elaborate on his thought process
Speaking to the first point, talking to clients about color, imagery, etc. is typically not useful. They don't speak in design terms. They speak in business terms. I frame all my questions around problems I am solving for my clients and then interpret them into designs I sell back by going through their points, one by one, confirming why this is the right solution.
Speaking to the second point, maybe there is legitimately a reason why he wants a photograph over your vector image. Having him answer this question allows him to give you insight into a problem he doesn't think your vector image is solving. Breaking this down typically falls one of two ways. One, they realize there really was not good reason besides their personal preference, or second, they have a legitimate business reason for their argument and you can now solve that problem. If it was personal preference ask if this login page is for clients or for him/her? I think you can see where I am going with that.
The point of this is we are problem solvers. In every situation you can always go back to asking, "What is the problem I am trying to solve here?" A vector may be the best path to solving that problem. Maybe it'll be a different vector then the one you have created originally. Who knows? You will. After you ask why. =)
Hope this was helpful insight!