Does it seem as though you are on opposite sides of the table when you discuss an issue that is important to you? Do you have a sense that you are being heard or acknowledged?
Conflict is normal in healthy relationships, it's based on mutual respect. The word 'fighting' here may be a red flag. Could be there is a better match out there :) It's difficult to resolve things with anyone who does not value the relationship as much as you do — or someone who is abusive (yelling, name calling, etc.)
Here's a link that best describes a healthy and unhealthy relationship link