Perhaps we say New Year's "resolution" because it's less binding than the word "promise." No one wants to break their promise. Everyone's pretty much OK with sundering their resolutions.
A better word would be "intention," but it carries no weight. Say you got married. Now imagine being asked if you "intended" to "love, honor and obey, until death do you part."
"Well, yeah, sure, that's my intention. But, you know, stuff happens."
It wouldn't work.
"Promise" has weight. "Resolution," particularly when it comes at the end of a period of sloth and gluttony, is the equivalent of setting your alarm earlier than usual but knowing you can hit the snooze button.
Still, some of us are full of resolve this time of year, intent on crafting a better version of ourselves. It's a laudable idea. Sure, we could all stand some improvement. But what you think needs changing might not be high on other people's lists.
You: "I'm going to set aside time every day to read a book and engage with the issues of the day, so I can make informed choices in my life going forward."
Your loved ones: "When you put a fork in the dishwasher, could you resolve to put it in the back part of the basket first so the basket fills up back to front?"