Rarely is anything truly "equally important" to both people.
More often than not "ego" and their past history play a part.
The first thing the couple has to decide is whether or not this is a "deal breaker" for the relationship or something worth getting divorced
One example might be he wants children now and she's climbing the corporate ladder with no desire to take a time out. Maybe it's over.
He wants to spend Thanksgiving with his family and she wants to spend it with hers. Is it worth going through World War III? Not likely.
In the beginning of (new relationships) we make the other person's happiness a top priority. Rarely does either person utter the word "no". We're always looking for a compromise or "win-win" scenario.
However when some couples go from a "Us & We" mentality to "You & Me" they tend to stake out battle lines, keep track of old wounds, and become invested in ("winning" against their mate) instead of "winning as a couple".
There are only two ways to experience joy and peace of mind in relationships: We either get what we want or we learn to be happy with what we have. Accept them (as is) or move on.
If it's a "deal breaker" - get out.
If it's not a deal breaker - learn to live without.
"Never love anyone who treats you like you're ordinary."
- Oscar Wilde
If you're with someone who is inconsiderate and always has to have things "their way" it means they don't think you're all that special.
Compromise is a sign someone sees the forest and not just a tree.