It sounds like you're in a difficult situation, and one where there is no clear right or wrong answer. What do you know about the history behind your partner’s opinion? Why does this person find masturbating offensive, and are there particular aspects of masturbation that are more offensive to them? Have you two had a conversation about how each of you feels, and why? If not, maybe you could start there. Ask your partner why they feel the way they do and whether masturbation is an absolute deal-breaker for them. These details may provide you with a more well-rounded idea of where he or she is coming from. There are a whole host of reasons why this might be a sensitive subject for them. In turn, be prepared to explain to your partner why you enjoy masturbating so much… what does it do for you? Can you see why your partner may view the activity as interfering with your sex life as a couple?
In general, masturbation is completely natural and can even enhance partnered sex. It gives us a chance to fantasize and experiment with what works for us, physically. Things can really heat up when a person brings the knowledge they glean during masturbation to the bedroom. As well, there is always the opportunity to incorporate masturbation into partnered play… Have you considered asking your partner to watch you masturbate?
Alternately, I have seen cases where one feels as though they have been replaced by their partner's masturbation. Knowing that their partner can so easily pleasure his or herself, they may doubt their own skills in the bedroom. You mentioned in your question that you do not feel masturbation is a replacement for sex. Does your partner know this? Have you two discussed your ideal sex life? And do you feel that those ideals are being met in reality? If you are both feeling heard and satisfied in your partnered sex, then where does the real problem lie? If masturbation is something that you don't feel comfortable giving up, let your partner know that. Perhaps your partner would feel more comfortable knowing that you will masturbate only when they are truly unavailable (away at work, travelling, etc.). This way, masturbation is less likely to be perceived as a replacement for sex with your partner. Find out if your partner is interested in experimenting with phone or cyber sex when he or she is away to help further include them in your masturbatory activities.
You may not change their mind, but having an honest discussion about masturbation with your partner may open their eyes to the ways it can help enhance and enliven your sex life, as a couple.