i don't think from what you said that he thinks its silly, more that he thinks it'll potentially cause you problems and upset in future- and its worth thinking long and hard about that, cos its a very expensive right pain in the arse getting those tattoos off again, and can leave you feeling really deflated and foolish.
you said you don't like confrontation- how are you gonna feel when the bajillionth person asks about it and then rolls their eyes at your answer? frustrated? undermined? embarressed? defeated? deflated? do you have a plan to handle this, are you conciously working on dealing better with confrontation?
what about your kids? how are you gonna explain it to them- how are they gonna feel holding mummys hand and then looking up and being told by her wrist to remember veal calves and battery hens? i'd guess maybe a bit sad. are you ok with that? is your man gonna find it hard to think of suffering every time he sees your wrist too? what if it screws up your intimacy or sex life?
what if something happens and you for whatever reason aren't able to be as veg*n as you want to, for some period- are you gonna have the problem of, and be able to handle feeling guilty and judged when you look at your wrist? are you gonna feel that way? are you gonna be able to handle other people feeling that way- both that you're judging them and their judging of you as a hypocrite?
i agree with poppy that something more positive might be something i'd personally prefer. also something less restrictive. i might go with something like 'remember', or 'think, feel, trust' instead. there are lots of other ways of conjuring the same passion on a personal level, that pique curiousity in others which leads to a productive discussion, but which also don't come with the same challenges, and negative conotations or implications both for yourself and for others.
at the bottom of it, its your arm. i'd do what i wanted with my arm, regardless of what my partner felt- and he'd accept that, regardless of how he felt about it, cos basically, its my arm, and i'm stubborn like that. but what you do does affect other people, and the whole relationship dynamic, so maybe some more discussion is in order- especially as your partner must be someone whose opinion you respect and feelings you care about, otherwise you'd probably not be with him.