This took me a long time to learn.
Hopefully this will help you learn it quicker than I did.
Perhaps an object lesson will speed it up even more.
Go outside and find a very small rock.
Something gnat sized.
Now remove one of your shoes and insert the tiny rock into your shoe, and put the shoe back on your foot.
Now wait a while.
At first it won't bother you. After all, it's just a small rock.
As the day goes on, the presence of that wee object becomes increasing noticeable, increasingly irritating, until the only thing you think of is getting rid of that rock.
You can't concentrate on much else, and the longer that stone is in your shoe, the worse it gets.
Now imagine if someone else had put the pebble in your shoe, and only he had the ability to remove it?
But every time you approach him to resolve the issue, he dismisses it because "It's just a small rock, and I have much bigger problems to solve."
I would suggest that this response does not warm the cockles of your heart.
Now imagine if this same individual came to you to get support for a big, new, important project he was working on.
You bring up the rock, which by now is aggravating a blister the size of Manhattan.
He tells you that if you support the project, which is "important", he may be able to have someone look into your issue. After all, no one else is complaining about it.
And he wonders why you are reluctant to support his project.
I hope you are good at metaphors and see that as IT leaders, we are very, very good at putting pebbles in other people's shoes.
If you ever wonder why people aren't enthusiastic about supporting your projects, you need to ask yourself if it may be because they can't ignore the irritants you have introduced into their life... Technology that is not reliable, program interfaces that are kludgy and non-intuitive, slow turn around times on service, unfulfilled promises, inaccessible support and service. These are irritants that you have the power to remove.
Perhaps you didn't put the stone into their shoe. But just maybe, given your team's exceptional brilliance and experience with technology, it would take a moment of your time to resolve their issue.
The good will it generates is immeasurable.
And perhaps they will be in a more favorable mood to support your project.
Especially since they aren't thinking about that damn rock in their shoe.