Just tell them what you told us. Explain your reasons. If they don't believe by any means. Well, that's out of your duty, your not responsible for that. I would highly suggest to not care what your friend thinks about your motivations. You have a goal, stick to it, follow it & become who you want to become. It doesn't matter what your friends thinks about your motivations. If it's very important to you to convince them. Yet, don't make it a discussion, just repeat your motives anytime that the topic came on, then pass, by your constant repeats they might finally swallow up the point.
People will rate you,judge you,will attempt to break you,but how strong you stand will makes you, "you". I know this might not fully be related, but i just wanna say you are who you are, as long as you have a goal, doesn't matter what others think about your motives,purposes & reasons & actions, you living life for yourself not for other's thoughts.