People who drive a hard bargain, fighting tooth and nail to get a good deal, using wit and skill to best their adversaries, are generally respected in our competitive individualistic society, and it’s satisfying to get what you want. Why not take this mentality into the romantic relationships as well? But skilled negotiators know that the best deal is one where both parties feel like they got something they really wanted and both had to give up something that was important to them. Ultimately, both walk away happy with the mutually beneficial result.
One of the unfounded fears in romantic relationships is that giving ground on a specific issue will weaken your overall position, making you seem like a pushover. Sometimes people are pushovers in other areas of their lives, like at jobs where they have to follow orders, and they unconsciously look upon their relationship as one sphere of life where they can wield some power and control the situation.
Whatever reason for not wanting to give in on some area of discussion, if you can separate in your mind this specific area from what is apparently being said about your character, you’ll be in a better position to see if giving ground is a good idea. One way to frame it to keep your dignity intact is to say “What I care about is the health of this relationship and both of our happiness, and I’m willing to do just about anything to make those things happen. I hope you are too.”
Standing up for yourself and refusing to let others walk all over you are admirable traits and they are probably part of what drew your partner to you in the first place. We like confident people who know what they want and are not scared to go get it. But there is a fine line between standing up for yourself and blind obstinacy, and this line becomes much fuzzier when you weave your conception of yourself into the fabric of the specific topic under discussion.
In a romantic relationship you can never really win a fight because the underlying combatant attitude puts the two of you at cross purposes and stirs up resentment. The only way you can win is by treating the relationship as a separate entity and deciding to work together as a team to make it as good as you can for the both of you.