Let´s see. I guess you can go whit the basic "people are usually very cognicentric and ethnocentric". In other words, what´s right or wrong depends on the internalized values of the culture that every individual is immerse in, as well as their own perspective and thoughts. So anything that doesn´t fit within the ideals of what a "normal" 15 year old should be doing, would pretty much always produce an aversive response and essentially disgust towards the "different one".
Rather than trying to convince others it seems that you are trying to convince yourself that it’s ok to like this show. And well, the truth is that only you can know what is and isn´t ok for you to watch. Anyone else´s opinion, especially those who would criticize you, are most likely reasoning the whole thing from a closed perspective based on whatever concept of normality and right and wrong they are dealing with. And since most people in our time are so desperate to fit whit the norm to actually get to know themselves, then no doubt there will be many who would disapprove of anyone your age or older watching a show conceived for little girls. But then again, nothing prevents you from liking it, nor does liking it prevents you from being a mature, responsible and functional adult or in your case teenager.
In conclusion the disgust towards grown people liking this show, particularly grown men, comes mainly from their incapacity to leave traditional conceptions of male sexuality behind and the tendency o humans to analyze everything from their own culture and their own un-criticized way of thinking. Which basically translates in most people thinking you’re a freak and/or a pervert and there is little to nothing you can do about it. So rather than trying to convince others whit reason and logic, enjoy what you like. Others will tell you it´s wrong but then again for everything that exist in this world there will always be those who would say it´s wrong. So live and let live, and try to tolerate their perspective, for however close-minded it can be.